I never saw one go full auto; mostly they won't even go semi-auto.
Seen a few in my day; One was brand new from a Woolco store. Guy brought it into the shop complaining about it going full auto. I told him it was not very likely that a new gun would do that. He said he would give me the gun if I test fired it and it DIDN'T go FA. I loaded it, pulled the trigger, and sure enough 15 or so shots zipped right into the bullet trap, much to my amazement. Kinda neat in a way, but we sent it back to Savage.
Another time we ran into a couple of guys in the Everglades shooting and having a ball with their FA Springfield 187.
I was given an old Stevens that needed a feed ramp assembly replaced. I made the repair, and when I went to test fire it, ZIIIIIIIIIIIIP. It got broken up for parts and sold.
Usually, they go FA when some of the internal parts wear. This is (IMO) due to the unusual design whereby the bolt is held back until the trigger is released.
Although 15 or 16 shots going downrange in one ziiiiiiiiiiiiiiip is amusing, you don't want to get caught with it.
Not a common occurrence I suppose, but it can and does happen.