I had a similar thing happen to my cat and my dog. I had to change collars on the cat to a different type. They have a kind that has elastic on it to break away from object. My cat got hers caught on branches and the window shades!!! However, leaving my animals WITHOUT collars is even worse. They look like stray animals if they ever got loose and can't catch them when they need a bath !
Scooby got his collar caught on a blanket that was on my couch. He isn't allowed to be on the couch. I found him when I got home hiding uder the bed. He was embarassed! He had this huge blanket dragging from his collar clasp!!! After I stopped laughing I set him free. Poor baby!