I've occasionally left my boys regular rope halter on, but by the morning its always gone... Somehow he gets it off... and its not breakaway...
He either un-halters himself, or he has a friend who helps! It is amazing to me what I missed before I got my horses in my back yard (2000). My two 5yo geldings love to play with one another's halters--I used triple-ply nylon Hamilton-types. "Buster" (5yo QH) will play with "Sweet Cup and Cakes" 's halter and I've watched
him work on it and undo it twice now.
I do not leave halters on my horses during turnout and never in a stall. If I go camping, they are haltered and teethered, but we prefer to use their leather halters for that, and they can break free with them. For regular stuff I use the nylon ones, but I do not fully buckle them, just hook the pin in the grommet, and I don't leave them outside of my sight. I've had >30 horses over the years, and I give my horses turnout probably 90% of the time. I have had several incidents of horses getting caught in the leads and panicking over the years. It is possible to undo the halters if they are not buckled, but you could get hurt if they are and the horse is scared.
The BEST insurance policy is to train your horse to ropes around their legs and to train your horse to relax when you help them. DH even told his horse, "Tyke" to sit down when he got his back legs caught while tied to a tree. He did sit. My horses all know, "open the gate", "field", "back up", "walk on", and other commands I've forgotten that I've taught them. If you add, "Come here," you'll never have to chase your horse again...probably!