No, your generosity will not mean that you have to keep it up when they move to a nursing home. Under the Medicaid rules, nursing home residents must contribute their income towards their cost of care, but only the income to which they are legally entitled. Once they move, you can continue to make payments for extras for them. Just don’t give them any money directly, since that could be construed as income to them. And, if they have long-term care policies, as you say, they may not need Medicaid in any case.
For more information about Medicaid's income requirements, click here.
For more about long-term care insurance, click here.