ALBION, Mich.—Phillip and Stephanie Mastin have lived all of their 40-plus years in this small manufacturing town set amid farmers’ fields. Neither, though, had ever attended a lecture or a basketball game at the private college near their home.

“There was just no reason for us to come here,” said Mr. Mastin, a former welder at a shuttered auto-parts plant who is now studying at a community college.

But last spring, the couple sat inside one of Albion College’s red brick buildings as their 18-year-old son collected a $45,000-a-year scholarship from the school.

The free ride, one of 13 given to local students in the past two years, is part of a change playing out at small, liberal arts colleges in beaten-down towns across the country. As they struggle with falling enrollments and difficult finances, they are realizing how their own futures are intertwined with the broader community.

“We can’t survive if this town isn’t healthy,” said Albion’s President Mauri Ditzler, who was hired to turn around the 181-year-old school. “And the town can’t survive without us.”