When someone is finally resting or accepting a
situation, after they've been fighting it. (Based on their use on hospital patients, who
may be fighting to pull out IVs or foleys, and so they put "big
mittens" on their hands so they can't hurt themselves, and they finally fall asleep.")
"Is your
friend still suing their landlord to
get their deposit back?" "No, she's decided to let it
go. She's sleeping with the big mittens on."