Related: Does anyone know of books about the night shift throughout history? About what had to be done at night to keep society going? Because it sucks, so it'd be nice to know I'm not the first person enduring it (I suspect I'm not). Please, message me the titles. I don't buy a lot of books but I might buy a few of these.

By definition, an inn is a place that provides lodging overnight, so they did not chase out their customers at curfew. If anything, their patrons came running in at curfew.

It depends ...

On where you are and when you are. Cities often had curfews, and anyone out after that time needed official reasons to be. One would have to research a particular place in a particular time. Outside the city, rarely such a thing as curfew, and then in the larger small towns or in the faubourgs. In the country inn, they made their own rules, according to the mood of the proprietor and the likely patrons.

Are you thinking of taverns, perhaps, places that provide food and drink but not lodging?