How does my claiming Mom as dependent on my taxes impact her Medicaid eligibility?

I'm a caregiver for Mom. My mom is 85 years old and has moderate Alzheimers. She can dress and take care of her personal hygiene. Her social skills are very good but she is very forgetful. She lives with us and we do all the cooking, shopping, transporting, and oversight of medical needs. She has some savings and her only source of income is social security and a small annuity which are less than the Medicaid requirement. At some time she will need more care than we can provide and we do not have the resources to pay for private care. Her savings will only pay for a few months of private care. I was told that if my husband and I claim her as a dependent on our taxes, that it will affect her eligibility for Medicaid since our assets would be considered.in determining her eligibility. Is this true? HOw does this impact her eligiblility when she can no longer live with me?

I am her POA. I do not want to be responsible for her medical expenses. Will claiming her as a dependent affect her eligibility for Medicaid or make us responsible for paying for her medical care even if I sign all things with my POA designation?