If a child purchases her parent's whole life insurance, will death benefits be paid upon the death of the parent?

Another thing to keep in mind....... The whole life policy should have a specific cash value, either placed annually or at a fixed date. That $$$ value is an asset of theirs. If they are going to apply to Medicaid, any transfer of assets poses a penalty for Medicaid. You would need to buy the policy to become the new owner & compensate them for the value of the policy to avoid transfer penalty OR they do not apply for Medicaid till 5 years plus has passed since they transferred it to you & beyond penalty.

GUL policies usually have a value too.

Term life policy doesn't have this asset sticky as its not worth anything till after they die. So those can change ownership - as long as their competent like GeeWiz wrote - with no medicaid issues. But what medicaid can do, if allowed by thier state laws, is require term over a certain amount to add on the state as a beneficiary so state can recoup Medicaid paid costs.
As an aside on this... What states seem to be looking at is having those with term policies to do a life settlement on term policy and require settlement $ to spend-down before medicaid could pay.

Death benefits are paid to the named beneficiary. The owner of the policy designates the beneficiary. Are you asking about buying a whole life policy on the life of your parent or an existing one from your parent? If your loved one has dementia, he/she isn't able to make a decision to sell the existing policy to you.