Yes I have acquired a boyfriends t-shirt to sleep in before. For me it's for comfort, I can smell his unique odour on the collar and I find that soothing. If I can't have him in bed snuggled up to me then being able to smell him as I doze off is the next best thing.
Ha hah! I just saw your question and I thought, hmmm, do women do that? Is it because it still has your scent on it and they want something to remember you by? When I was a teenager, I loved it when a guy lent me a shirt or held me and when he let go it still has his smells, whatever they might be on them. MMMMMMnnnnn... Freaky, I know, but I love my guys scent. Although, I never stole his shirts. That, you've got me on. When you find out let me know. Maybe they just needed clothes...
I did this as a teenager but I asked the guy first. I loved wearing his shirt because it smelled like him or his cologne. It made me feel closer to him when we weren't together. It wasn't a trophy in my eyes.
Yes, for some reason women like to take a guys cloths home? That's why I only let them wear the shirts I don't really like. Sound harsh? I have given all of my old band t shirts to my little sis. I'd rather she had them.