Panera Cares Community Cafe opened in Center Plaza, with a pay-as-you-can approach. "I'm homeless and still gave, cause I want others to have," said Wayne Gilchrist, who lives under a bridge in Cambridge, Massachusetts.

Panera Bread opened a pay-what-you-like location in 2010 in St. Louis, Missouri, to much buzz—and some confusion. Customers and industry watchers scratched their heads, wondering how a menu with no fixed pricing would work.

The latest pay-as-you-wish operation debuted in Boston more than a year ago, and there are now five community cafes, called Panera Cares. The special cafes are the brainchild of Panera Bread Chief Executive Ron Shaich, and offer a case study in how a for-profit company is navigating philanthropy and bottom lines.

In addition to running a chain that includes 1,800 regular cafe-bakeries, Shaich has made battling domestic hunger and food insecurity a priority. Shaich (pronounced "shake") at one point lived on $4.50 a day. Food insecurity includes families who don't have reliable access to regular meals.

But whether the private sector can help solve food insecurity through scalable solutions remains to be seen.

"It's a mixed picture," said David Spielman, senior research fellow with the International Food Policy Research Institute. "A lot of companies have sustainability strategies. Not every company has the wherewithal to pursue real sustainable strategies, social or environmental," said Spielman of the Washington, D.C.-based group that's focused on studying hunger and poverty.

Researchers and for-profit companies are seeking solutions as domestic food insecurity remains at the highest recorded percentage—14.5 percent or roughly 17.6 million households—since the U.S. Department of Agriculture began monitoring the issue in 1995.

Read MoreIt's getting too expensive to be poor in America



It has been five years since the 2007-09 recession. But food insecurity remains stubbornly high. This despite lower unemployment levels because families now are battling higher inflation and rising food costs, according to a USDA update on food insecurity released last month.

"Food insecurity remains a problem," said Alisha Coleman-Jensen, a researcher with the USDA. Prior to the recession, the percentage of food insecurity hovered around 11 percent—3.5 percent below the current level.

"We've also seen some moderate income households that have food insecurity," USDA's Coleman-Jensen said.