I have seen posts on this forum on occasion from people looking to buy the private keys to old addresses which used to contain large (by today's standards) amounts of bitcoin. The only reasons I can imagine that someone would want to buy such a private key would either be to lend credibility to a lie that they have been involved in bitcoin for longer than they really have, probably so they can attempt to scam someone ("I've been involved in bitcoin for years and handled hundreds of BTC, look at this signed message as proof!"), or so they can claim that those old transactions represent bitcoin that they have sold, probably for tax evasion purposes or perhaps if there are debt collectors after them.
Exactly.
Nothing good will come from this.
Do not sell your old addresses private keys. Specially if you sold them in an exchange and somehow those addresses can be tracked back to you.
You may sell to someone who is trying to laundry money or something like that, due to some illegal activity. If they buy your address and some authority track that address back to you, you may have problems.