Unlikely use case, but since I've heard of more ridiculous ideas that actually worked...
If I had an address from years ago, and could sign it to prove ownership, I suppose I could fool some people into thinking I was the original owner, and therefore also owner of any identities online linked to the address. That buys me reputation, at the very least? Even some clout if the address used to own 40 BTC. In the eyes of some, anyone who was daring enough to use Bitcoin in those days is probably someone whose opinion counts.
This is unlikely to be the case, since these people typically buy more than one address. If all you wanted was clout, then you could just buy one single high valued address and be done with it.
Odds are people are just looking for forked coins, and hoping that the owner doesnt notice they are available. Often these people can tell you in advance if they want your address, likely because they are using a service like:
http://www.findmycoins.ninja/ before deciding whether to buy.
