I think I posted a somewhat similar experience here a few years ago.
I was playing golf at my club and as we walked up to the 15th tee, we saw a doe Muley which had tried to jump an iron fence and didn't quite make it.
One of her hind legs was caught in the fence and she was stuck.
I climbed over the fence, talked to her softly, rubbed her neck and told the others in my group to lift up on the hip of her stuck leg while I calmed her. When they did, I was then able to lift her leg up and over the fence and she was free.
She didn't try to fight me at all because I think she knew I was trying to help her.
She was bleeding a little, but nothing serious. So when I opened a gate on the other side of the homeowner's yard, she was limping a bit, but otherwise no worse from the wear and she ran off.