This actually happened in my game a couple of years ago.
Clever Player: (puts on a strange-looking pewter ring)
Me, the DM: You feel queasy, and sick to your stomach. You try to remove the ring, but it won't come off!
CP: Aw man. It's cursed, isn't it?
DM: Yep. Until you break the curse, you can't benefit from a long rest. You will weaken and die within a week.
CP: I have a better idea. Morogast, I need you to chop off my finger!
Morogast: Huzzah! I ready my sharpest blade!
DM: ~sigh. Fine, the barbarian cuts your finger off, ring and all.
CP: Ha-ha! So long, evil ring! I throw it in the campfire and go to bed.
(the next morning)
DM: You wake up feeling exhausted and queasy, with a point of exhaustion.
CP: Huh? But I cut the ring off my finger!
DM: And your finger is still gone. But you notice a strange-looking pewter bracelet on that same hand.
CP: ...fudge.
(only he didn't say "fudge.")