Can full-time caregivers get health insurance?

My uncle is thinking about quitting work to take care of my grandmother (his mother) full-time. She is diabetic, blind, and unable to walk more than a few feet a couple of times a day. He's been working full time and caring for her full time. As she gets worse, it's getting to be too much. He can take 12 weeks of Family And Medical Leave, unpaid. But would he be covered by his employer's health insurance during this time?

If he quits his job entirely, can he get coverage from any other resources?

She has a small annuity, some savings, and Medicare coverage, so it's not her living costs we are worried about, but my uncle's health care coverage.

We try to pitch in and help as much as we can. But it's a full-time job (and then some) to be a caregiver. What can we do?

We live in Arkansas.