If the person gifts the money to the payer, then the payer cannot claim tax relief on it.
The Financial Assessment for the Fair Deal Scheme adds back any gifts given within the last 5 years.
If the person paying the fees is going to get a bigger inheritance, it makes sense.
Otherwise, it probably doesn't.
If you pay my fees of €60,000, then I will have €60,000 more cash and so in each of the following years, the state will pay 7.5% less or €4,500
If the state is making no contribution anyway, because I have a valuable house, then it might make sense for a relative to pay it.
Brendan