Historically, the field has been made up mostly of women, particularly women of color. Today, men make up just 14 percent of the direct care work force. But the number of male home care workers is rising — tripling to 182,000 in 2015 from 60,000 in 2005. Home care work is where the biggest unmet demand is expected.

So how are more men recruited into a field historically dominated by women?

Bottom line: If you want to recruit anyone into this field, men included, you have to raise wages. The median hourly wage for home care workers in the United States is a little more than $10. The median annual income for home care workers, most of whom work part-time or only during part of the year, is $13,800. (A majority of those surveyed said they would like full-time work.)

Retention is a huge challenge. “There are no reliable statistics on turnover in this sector, but our estimate is that it’s somewhere around 60 to 80 percent,” Mr. Espinoza said. “That’s devastating for the workers and the families that benefit from their care.”

While wages remain low, strides have been made in job protections. The Fair Labor Standards Act, originally passed in 1938, exempted home care workers from overtime protections, claiming they were mere “companions.” But in 2010, a coalition of organizations finally got the law amended to cover home care workers.

“This work force sits at the intersection of two cultural problems,” Mr. Espinoza said, “the devaluing of working-class women and the devaluing of older people and people with disabilities. That confluence of sexism, racism, ageism and ableism means the sector gets ignored.”

Studies show that when women enter fields in greater numbers, pay declines. Could the reverse also be true? Could more men in direct care work help boost wages for everyone? Paula England, a sociologist and professor at New York University, thinks it’s possible. “It’s a logical extension,” she said. “If the reason pay goes down when women go in is that employers somehow devalue it, you would think that would operate in the reverse. As men go in, we would see that work as substantial and more important. But we don’t really have examples of that.”

The quality of care jobs will have to rise to attract more workers, and the pathways to get hired have to be redesigned. An interesting example is to be found in Albany, Minn., at Mother of Mercy Senior Living. Facing both the general shortage and the particular challenges posed in rural communities with dwindling populations (Albany has fewer than 3,000 people), Mother of Mercy’s leaders struggled to recruit workers for years.