I'm interested in circulation so when I something like this appears, it gets me going. I know it's 30 years old, but how many times does a coin like that have to change hands to degrade to that degree? And it's a 40%er so I'm surprised it didn't get plucked by some CRHer or someone in that amount of time.
My hypothesis? I'm glad you asked

: it related to my theory of Island Geocirculation (with apologies to MacArthur and Wilson). Briefly, it works like this. If you live on an island that is isolated from the mainland and there is little migration of coins in or out of the island, then coins wear down due to daily circulation. Paper doesn't last, so coins are used. When an Ike or JFK is in the isolated population, it may change hands on a daily basis. Small islands, more circulation. The more isolated, less migration. It wouldn't have to be a real island, just an isolated (arctic or jungle), closed community.
Or maybe it was a pocket piece belonging to a nervous guy whose hands were always in his pockets.