No, your assistance to your parents does not affect their eligibility for these programs.
Programs like PACE, Medicare and LIHEAP use the income of the participants to determine the level of benefits. By helping your parents, you are not adding to their income, therefore you are not affecting their eligibility or the amount or taxability of their benefits.
However, in calculating whether they qualify as your dependents, the amounts paid by these tax-exempt programs count as part of the cost of their support. To be your dependents, you must pay half or more of their living expenses, but they do not need to live with you.
Here are rules for claiming a dependent. The IRS provides a worksheet for determining support that explains what counts.
