In NYC, do retirement assets count against Medicaid/Medicare eligibility?

My mom is 67 and retired. She has an annuity with an IRA in it and it has been sitting there for many many years and it has matured. She is worried that it would affect her Medicaid and Medicare eligibility but to my understanding her Medicare is guaranteed due to age regardless of assets and income and her Medicaid should be fine as long as we don't distribute any or too much money out from the annuity and exceed the income limits for medicaid eligibility. Can people confirm if I am correct?

For the next question I have which I doubt most people will be able to answer but figured maybe someone might:

I'm considering doing a 1035 exchange for that annuity to get her a better rate while also avoiding a distribution. While I don't think just owning retirement assets would count against her medicaid eligibility nor would an annuity exchange count as a distribution and add to her income and exceed the Medicaid income limits, I just want to double check that. She's insisting on doing a lump sum distribution and giving it to me because she is sure having any investment/retirement asset will have her lose Medicaid and I have to keep telling her she's going to raise her tax bracket substantially and lose Medicaid anyway since the distribution will be counted as income.

submitted by /u/Alternative-Bend-396
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