It happened to me, although it was a long time ago, and things have changed. I was en route going from the UK the long way to Australia. I was scheduled to change places in Los Angeles and we were diverted to Las Vegas. Due to the rules about crew flying times, etc., I had an unscheduled 24 hour stopover. Then instead of direct to Melbourne it was Honolulu, Papeete, Auckland, Sydney, Melbourne.

In our case we got processed, and and assuming nothing flagged up you were given a temporary visa, told not the leave the city, and told to be back by a certain time. Or else.

But times have changed - I don't know what would happen now.