Burger King (at least the last one I went to) has a poster saying that their burgers are available during breakfast hours.
There are some fast-food chains that don’t have a breakfast menu at all. I don’t think Wendy’s does breakfast, for instance. Can’t remember how early in the day they open; the nearest Wendy’s isn’t exactly close by.
That was the default until recently. A couple years ago Wendy’s dropped mustard from its standard condiment package for the Single/Double/Triple sandwiches. Sacrilege! But mustard is still standard on the Jr. Cheeseburger (along with ketchup, onion, and pickles).
At my local Wendy’s I order a Single my way (cheese, ketchup, mustard, and lettuce) and they hand me a packet of mustard on the side. I can’t figure out why they can put the mustard on the Jr Cheeseburger but not on a Single!? 
The ones mentioned above plus Carl Juniors, Subway, Filibertos, Denny’s, and others. It’s pretty much the norm here. I was a long time third shifter. I never had much trouble getting lunch whenever I wanted.