The message after a mass shooting, this time at a Texas elementary school, was clear: People who want to curb gun violence should “cast their vote in November.” That was how Senator Chuck Schumer, the Senate majority leader and Democrat of New York, put it on Wednesday.

But not everyone will have to wait until then. On June 1, when the shareholders of the Connecticut-based gun maker Sturm Ruger log in to the company’s virtual annual meeting, they can vote on a shareholder proposal that states because of “the inherent lethality of firearms,” Ruger must hire an outside firm to study its impact on human rights, “above and beyond legal and regulatory matters.”

The human rights study is an unlikely crusade at Ruger, similar to an effort at Smith & Wesson, another rare publicly traded gun company in a largely privately owned and opaque industry. The nonbinding proposals pit a nun, who is leading one activist group, and a hospital executive, leading another, against gun makers who have so far been unwilling to compromise.

They may not be typical Ruger investors, but they are representative of a certain kind of activist investing: buying shares in a public company in order to have a say in how it is run.

Shareholder activism can mean several things. Some activists want to take over a company and govern it differently for financial reasons. Some, like the ones urging Ruger to study human rights, invest in companies in order to push them to change on social issues.

On Wall Street, the field of E.S.G. is expanding. That stands for environmental, social and governance issues in corporate stewardship, and making decisions with an E.S.G. viewpoint leads some investors to avoid certain industries, like fossil fuels, private prisons and tobacco, while others agitate for change within organizations.

In Ruger’s case, a group of investors led by CommonSpirit Health, a nonprofit hospital chain based in Chicago, wants the company to do a human rights impact assessment on its products and business practices. The push is part of a larger effort coordinated by the Interfaith Center on Corporate Responsibility.

Ruger representatives did not respond to calls and emails seeking comment.

“If we can move corporations, that is a really big leverage point for systemic change because of the money and power that corporate America really has today,” said Laura Krausa, CommonSpirit’s director of advocacy.

Ms. Krausa and her allies have little to lose and a growing precedent to follow for successfully nudging companies’ behavior.

The increasing focus on E.S.G. issues has led banks and other financial companies to pare back financing of the dirtiest fossil fuels. It has also forced myriad companies to diversify their corporate boards by adding more women and minorities.

The changes brought about by individual shareholder resolutions have not been momentous on their own. But together they have pushed companies to greater awareness of how their actions affect the wider world.

Shareholders’ willingness to vote in favor of E.S.G.-oriented proposals is rising. In 2021, for instance, 44 percent of shareholders in Smith & Wesson voted in favor of an investor proposal that the company adopt a human rights policy. That was higher than the 36 percent of shareholders who supported a similar proposal filed in 2019.

“It’s kind of a Hail Mary,” said Dr. Jonathan Metzl, the director of the Department of Medicine, Health and Society at Vanderbilt University, whose research focuses on guns in America. Shareholder resolutions are weak, Dr. Metzl said, because they can only influence one company at a time and, without broader, more coordinated pressure, individual gun makers have no incentive to act.

Ruger opposes the current proposal on human rights and has described CommonSpirit’s interest in the actual day-to-day business of the company as tenuous.

“Despite minuscule ownership of company stock, the proponents are using the proxy system to advance the gun control agenda they have been unable to achieve through legislative and other means,” Ruger wrote, urging shareholders to vote down the proposal.

Even if it passes next week, the resolution will not force the company to act. But the view of activist investors is that any kind of influence over the gun industry is better than none at all.

The recent history of agitating for change from corporations, as gun control advocates tell it, is largely a history of failure.

When Ed Shultz, who was Smith & Wesson’s chief executive in the late 1990s, struck a deal with the Clinton administration to adopt new safety measures for its products, retailers and the National Rifle Association boycotted the company and almost bankrupted it, driving Mr. Shultz out of the industry.

When companies like Citigroup, the retailer Dick’s Sporting Goods and Delta Air Lines have declared support for gun control measures and vowed to promote gun safety by changing their own business practices, groups like the N.R.A. have campaigned against them.

Investors, though, can be harder to ignore. Boards have a duty to listen and respond.

In 2018, a measure urging Ruger to produce a study on the safety of its products won a majority of shareholder votes and the company responded with a two-dozen-page report.

“The criminal misuse of firearms is a complex societal issue, resistant to solution through more laws or new technologies,” the report said. “We have long warned that there is no such thing as a foolproof gun, and there is no substitute for personal responsibility and common sense in the safe handling, use and storage of firearms.”

Activists said it did not actually answer their questions, but at least it was a start.

Some investors also have campaigned to remove Ruger’s board members, including Sandra S. Froman, the former National Rifle Association president whom the left-leaning group Majority Action revealed had worked with the eugenicist William Shockley in the early 1970s to make his theories about the inherent inferiority of Black people publicly palatable.

Ms. Froman said at the time she did not remember working with Mr. Shockley.

Efforts to create board turnover failed. And Ruger and Smith & Wesson tried fighting back. When the investor groups first began proposing shareholder resolutions, the companies appealed to the U.S. Securities and Exchange Commission to try to get them stricken from their agendas. The S.E.C. refused.

But after that, a surprising thing occurred: Ruger and Smith & Wesson both started talking to the investors who had made the proposals.

“We didn’t imagine it could ever happen,” Ms. Krausa said. “I don’t think that these companies typically engage like this.”

In 2019, CommonSpirit first proposed a human rights assessment similar to what is on Ruger’s proxy this year. Ruger offered to engage in a dialogue if the investors withdrew their proposal. They agreed. But the company insisted that they sign nondisclosure agreements before the talks. Ms. Krausa said CommonSpirit declined when Ruger asked to talk under the same terms earlier this year.

Sister Judy Byron, a nun who is a member of the Adrian Dominican Sisters, another shareholder in Ruger and Smith & Wesson, said she looked to past victories spurred by shareholder activism for inspiration. Resolutions beginning in the 1970s urging companies like General Motors to stop doing business in South Africa bolstered the anti-apartheid movement, she said, though nearly two decades passed before their goals were achieved.

“I’ve been doing this work now since 1998 and I’ve really seen the support of other shareholders, the vote, go up,” she said.

Sister Byron and the Adrian Dominican Sisters do need additional support from other investors, and that support is far from guaranteed.

Big asset managers like BlackRock, State Street, Vanguard and Charles Schwab as well as the quantitative fund manager Renaissance Technologies make up a large portion of Ruger’s shareholders. On Wednesday, Ms. Krausa emailed some of these large shareholders asking for their support.

Representatives of each of the companies said that they could not comment on how they would vote. But on Thursday, Vanguard executives held a phone call during which Ms. Krausa and others made their case for the assessment.

BlackRock voted against a similar measure proposed for Smith & Wesson in 2020, noting in a summary of its voting decisions that year that “the request is either not clearly defined, too prescriptive, not in the purview of shareholders, or unduly constraining on the company.”

Brian Beades, a BlackRock spokesman, argued that BlackRock’s holdings of Ruger did not mean the company had taken an investment position on guns.

BlackRock has found its own ways to express concern over gun companies’ governance. In 2018, after the school shooting in Parkland, Fla., where a gunman killed 17 people, BlackRock announced it was “engaging” with gunmakers to ask questions about their business practices. It said that its discussions would remain private.

In 2021 it voted against re-electing the Smith & Wesson director chairing the company’s corporate responsibility committee over concerns with how the company acknowledged the risks posed by gun violence. It lodged a vote against a Ruger director for similar reasons. But the votes were not part of any coordinated campaign and directors still won a majority of votes.

Advocates like Ms. Krausa know a human rights report is far from a law that would, for example, ban AR-15s or require people to be 21 to purchase a semiautomatic weapon. But they see it as better than the current posture of heads in the sand.

“This resolution is poised to help the company understand their role in addressing what is a crisis of colossal proportions,” she said of CommonSpirit’s human rights assessment proposal.

Dr. Metzl saw only slim prospects for change. It did not help, he said, that gun stocks have flourished during the coronavirus pandemic, when gun sales shot up and images of people waiting in around-the-block lines to buy them prompted manufacturers to increase their production.

“We should try everything we possibly can,” he said, “but I would say if this is the only avenue it’s a reflection of a much bigger problem.”