How many of your children do you still have to put through school? It’s difficult being in that too wealthy for aid but not rich enough to pay full price bracket, especially when you have multiple children. If you tie up money for a relative for the next 3-5 years (or more if you end up having to repay them), how will that impact the college choices for your own children? Would repaying the loans impact your retirement?
I wouldn’t commit to repaying loans for someone else. I’d also be careful about offering a large gift unless you can do it every year until this relative graduates. How many relatives do you intend to sponsor in this way? Is it likely to cause hurt feelings if you help one but can’t afford to do the same for others?