We'll all get to experience finals week, whether it be first-hand or not. Here are just a few tips on how to handle being on the outside of the stress of finals.
When you notice someone's stress:
You might want to offer to buy them coffee (if you can afford it). Along with the coffee, or even without coffee, just offer to listen. They might just want to complain for a few minutes, so let them.
When you see them crying or notice they have been crying recently:
It probably won't make sense where they're getting emotional or why, but maybe you could just hug them and offer a cozy, blanket-filled study session. That would help brighten their mood and it wouldn't interfere with their (very necessary) studying.
If you happen to notice they're wearing the same outfit that they have been for a few (or more) days, or they're wearing something that isn't really a full outfit:
They probably haven't done laundry since before Thanksgiving. Just cut them some slack. That will change after finals are over.
If they're acting differently when you're out in public with them:
Stress changes the way people react to everything. Being put in social situations when someone's entire mental state is fragile will impact their normal behavior in big ways. And, to be fair, they likely haven't left their room in a few days, maybe not even when they need to eat, so they probably should learn how to be social again anyway.
If you notice them ignoring responsibilities, or avoiding necessary studying:
Just try talking to them one-on-one. They probably just need a little push in the right direction. Maybe even offer to study with them if you'd like.