There are two types of bear snares used. Most common is a foot snare. The other is a neck snare used in a bucket with a thrower. Those have the diameter of a 5-gallon bucket. The foot snares also use a thrower, about the same diameter, maybe a little smaller. Neither of them could possibly get past the shoulders of a bear.
Probably the bear was tangled up in some wire.
Largest snare loops you will find are wolf snares but they would at the most be only slightly bigger than the bear snares I described. I can't see them getting past the bears shoulders either.