I don't think there's enough info here to really provide sound advice. The best approach in these situations depends on a lot of factors, such as:
Age of Parent
Current health (which sounds like it is great)
Financial Status, e.g., do they have
- Large amount of liquid assets
- Other properties
- Long-term Care Insurance
- Pension or other regular income
If selling the house, what is your parent's tax exposure.
Nonetheless, you need to have a plan to cover situations where your parent's health takes an unexpected turn. In-home healthcare assistance is expensive but usually manageable. Assisted Living in facility is even more expensive. Nursing care is ridiculously expensive. The latter two expenses can wipe-out a lifetime's worth of savings very quickly.
Long Term Care policies vary greatly, but in general are only designed to cover expenses equivalent to about 5 years of nursing care. Once that money runs out, there is no more.
The worst thing that could happen, from a financial standpoint, is that your parent's health get so bad that you are left with no choice other than to place them in skilled nursing care facility which causes them to burn through all their liquid assets. Before they can receive Medicaid coverage, they will be required to liquidate and expend all assets EXCEPT for their primary residence and a vehicle. So, liquidating the house now will remove that protection.
Keeping the house now will also be a problem if it is left vacant, as the house will likely deteriorate and insuring an empty house = $$$$. So there is no easy answer without know more about your parent's finances.
If all of this is making your head spin, you might consider getting some advice from a professional advisor who specializes in such things. Many times, you can find a social worker who will help you navigate this maze free of charge.
One additional note… if your parent is still lucid, this is a great time to make sure all of their legal affairs are in order (Wills, POAs, Medical Directives, etc.) and make a list of all their financial accounts (checking, savings, brokerage, insurance, etc).