Are caregivers allowed to live in low-income housing with the elderly person they are caring for?

Yes, you need a letter from your Mom's physician stating she has the need for a live in aide/care giver. Present the letter to the site manager or management company. You will need to complete a live in aide application & pass a criminal background check. The live in aide's income nor assets are not counted to calculate the rent. A live in aide can be a friend or family member. This is considered a reasonable accommodation.

I am guessing that the laws/regs vary from state to state so check with the powers that be that rent to your mom. My guess is that the answer will be no.

That IS a good question. a couple of months ago I was looking into options of living with mom or at least on the same grounds of various assisted living/nursing facilities but didn't get far in that quest.

Interesting question-I would check this out with the housing authority municipality in the area you are planning to do this-as the rules and regs can possibly be different---Or- check out senior housing options thru you local chapter on aging.
Good Luck!
Hap