Until the last dog is hung describes staying somewhere long after others have left, to stay very late at a party when others have gone home, to attend a concert, sporting event or social gathering and be the very last to leave, to persevere until the end. The idiom until the last dog is hung has been in use since at least the mid-1800s, though it may be older. The word dog, in this case, refers to a human. Petty thieves and indigents have been referred to as dogs since the fourteenth century. It is tempting to believe that to stay until the last dog is hung is a reference to a massive execution event, in which criminals are hung in succession.
https://grammarist.com/idiom/until-the-last-dog-is-hung/

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Note added at 1 day 4 hrs (2021-04-27 13:45:53 GMT)
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When I came home late, my father would ask me if I had to “stay ’til the last dog is hung.” I knew what the correct answer was and also what answer he wanted to hear.

Where did this expression come from?

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There are a couple of theories about the origins of this phrase, both pretty gruesome. One goes back to medieval times when, apparently, they used to hang animals for misbehavior, so it wouldn’t be unusual to see a dog hanging from a pole.

The other — more likely one, in my opinion — goes back just as far, and the dog in this case is human.

We’ve long referred to scalawags and scofflaws as “dogs.” And when hanging was in vogue, they believed in hanging in bulk. On a given day, the gallows would be in continuous use. Since hangings were public, the crowd used to stick around until the last convict was hanged.
https://www.eastbaytimes.com/2007/06/09/the-last-dog-hung-sa...