Shouldn’t our objective be avoiding emergency shelters?
Even so, it would be smart to include them as plan B or C.
It really shouldn't be that hard to tweak whatever bug-out-bag system you've adopted so it also serves a "survive emergency shelter" plan B purpose. You probably have earplugs, reading light and games/reading material in there already, as well as hand sanitizer, medications, toiletries and the like. If it's not there already I'd add something to eat and drink with (spoon, cup), and think real hard if the sleep-on-concrete-floor scenario warrants some inflatable pillow or if you make do just fine by resting your head on whatever clothes you're not wearing.