Is it broken or did the tuning screw go loose? Also some piano notes have up to 3 strings to make the one note so it could be one string making a funn noise. It's pretty easy to pull an upright paino apart to have a look. It's evan easier if its a grand!
Anyway, sure it happens! It's rare but not uncommon. As Ronster said, just cut it off so it doesn't rattle against other strings. And as he said if it's a higher dual or triple string, you may get away with just cutting it off. It may be quieter but you might be able to get away with it!