My childhood JRT did this! My brother and cousin took her out and she chased a rabbit into the burrow, except she was rather fat and got stuck. My dad and uncle went up with shovels, but were afraid to hurt her so it took a long time to gentle scrape away soil until she was free.
Laid back Lab decided to rip open his dog food which was sitting in the kitchen waiting to be packed as we were about to leave on holiday. He ate 4kg before he realised he was full and I saw him lying on the lawn looking rather bloated. Didn't fully realise until I saw the the hole in the back and weighed it to find it short. Vet advised it would come out eventually. Which it did over the course of the next 24 hours, and not in a solid state either. That was an interesting caravan holiday! Same Lab decided, on another caravan holiday, to roll in a very dead sheep, and we had to share a car with him on the journey back to the caravan before we could get him in the shower. He had previously found a wild camping ground and rolled in the area the previous campers had been using as their toilet. That was an unpleasant showering experience for both of us but the dead sheep smell was infinately worse.
He was a brilliant dog, very laid back and well behaved - normally but he had his moments. One day he wandered up to some fishermen to say hello, got some pats and they were very taken with him (he was a very calm dog and not intrusive) but he got a whiff of their sausage roll lunch and on his way past to return to me swiped the bag and wandered off, scoffing the rolls!
He fell down a rabbit hole and broke his leg. 2 miles down a country path away from the car. Poor DH had to carry him back. He was 45kg of pure yellow labrador. I miss that dog so much. Such a character and a sweet, gentle soul.
After he died his brother was very depressed. He went on to develop a condition common in labs where the vocal chords paralyse. Late one evening it happened and he couldn't breathe. It was awful to witness, he was panicking and gasping desperately for breath. We got him into the car and i stayed with him in the boot, and we went to the emergency vet. He kinda fainted and that released the paralysis, he started to breathe then. The vet sedated him to stop it happening again and he went for an operation. We had him another year and I was very grateful for that.