Is a restaurant still open after the kitchen has closed?

Recently a customer asked me, "What time do you guys close?"

We had in fact been closed for more than an hour at this point, which made it an awkward question to answer. I boldly forged ahead, remarking that it really poses the question, is a restaurant still open after the kitchen closes?

The kitchen has clearly posted hours. They are our hours of operation, and they are printed on both doors. However, the front of the house is in an awkward position in terms of trying to close a restaurant when two customers are still at their table and they are having the best conversation of their lives!

The kitchen produces food, which is at the center of what we do as a restaurant. Without that it's kind of like a shoe store being open but not having shoes to sell. You can come inside to get out of the rain, and you can even sit at a table and maybe get one more round out of the bartender. That's if your shoe store even has a bartender!

So here is the question: Does a restaurant turn into some kind of hang out lounge after the kitchen closes? The type of place where you can be the only customer but it's totally cool, they would be here anyway because they are still open?

Or is it closed?

If a place is closed, is it up to the customer to make that decision? Or do we have some authority as front of the house staff to kindly inform people that the place is closing and they will have to continue the greatest conversation ever somewhere else.

Don't these people know that a venue change can really spark up the conversation anyway?

As always, I crave your input so please leave your thoughts in the comments below.