Your scheme is absolutely, definitely, 100% impossible, because: any excess amount refunded must and can only go to the purchasor, the rich relative.
So that's that.
Note however that regarding the first-explained aspect of your Caper, the answer is positively yes. A primary reason (rich!) people give 1st class tickets as presents is that they are totally flexible. If one is ever lucky enough to get a 1st class ticket somewhere as a present (it's certainly never happened to me, tragically!) you can just call the airline and change anything you want. Yes sir, no sir, three bags full sir.
However, here's some astounding information on this:
Thanks to DC below, it appears that some (all?) airlines now offer "cheap, incredibly crappy" first class fares. in the Lufthansa example, I checked near dates and they only offered what (I would have thought of as) ordinary 1st class fares (to wit: obviously one can utterly freely change anything one wishes, at any time). However, a couple of weeks out, you can buy these "Easyjet-like" first class fares! :) which have restrictions and change fees and the like. So, consider this factor when implementing the Caper described by the OP.
Note that, with for example a €6000 "real" 1st class ticket given to you by the rich relative, after you refunded it, paid the €500 fee, and bought a €308 cheap ticket on a discount airline instead, you'd still be ahead €5000 in this "caper" suggested by the OP.
But again — very simply — all refunds today go only to the purchasing credit card, so the Caper wouldn't work. Thanks again, DC, for this "first class information"!