If the person who filed a restraining order doesn't show up for court what happens

Depends, what is this court date for ?

Why can't they show up? In Hospital, on emergency trip?

It is very possible that the court date will just be reset and the order will remain in place.

I would ask, why does it matter, if there was one, and it ends, it is best to remain away, since it is very likely just to cause more trouble to go near someone, who does not want to see you.

If you have an attorney, he may ask for it to be dismissed, but if they have not missed other court dates, it will most likely just be reset

If they don't show up, most likely the restraining order will be lifted.