How do I apply for financial assistance as a caregiver for my mother in law?

I agree with JoAnn. Some people do get paid through state programs. There is talk of making home caregivers more paid in future as in facility care is so expensive. However, the work is 24/7 and the care needed is grueling work. And you cannot get paid a living wage no matter how it is worked out. Often we see caregivers who gave up jobs, moved in with parents. They end with all parental assets and resources long gone, with bare subsistance living, and with no job and a home that Medicaid is clawing back sale price on for the care the state taxpayer has given. We have actually seen people in their 50s destitute and asking "Where can I go; what can I do" and the bad answers are that there are shelters. You have to get a job. You have to work up to affording a room in someone's home, then a studio apartment.
You need to think on this a lot before making a decision to do in home caregiving to and elder. Only you can make your final decision, but it should be as informed a decision as you can. Do look up medicaid for your State and see if you can get paid, for how many hours you can get paid, and at what salary can you get paid. There are many articles on AgingCare. Go to the top timeline and click on "care topics". Under alphabet you will see many. Some involve getting paid as a caregiver.
I wish you the best.

There is really no way to get paid. MIL could pay you but u say she has Dementia so she is not able to sign a contract. Depending on her income and assets, she may be able to get in home Medicaid. Your state may pay you they may not. Office of Aging may supply aides but that too is based on income.