I had to draw a lot to explain this, so here it goes. Its easier for me to draw than to writte. Took me longer, sorry.
Normally it is very rare for main sails to jam because they normally run on tracks and are often pulled by halyards. So if a halyards breaks the sail comes down.
Jaming is normally due to bad routing of halyards inside mast causing them to get stuck, normally happens when main halyard is pulled by another halyard inside mast, and "locks" on the sheave (so sometimes releasing everything might be the best bet), or track malfunction.
Normally stuck main sails happen more often on mast furling type arrangments, and these don't have battens.
In 1999 a friend of mine, António, sailing alone from Açores to Lisbon, on a 30foot Swedish designed boat, that had Selden mast with a hook for the main halyard had his main stuck all the way up, when the halyard "jumped" the sheave.
He needed to reef at some point and ...bad news.... no luck
He showed up a few days later with his main wrapped around the mast as shown bellow. This was his solution. He sailed with genoa only for 580 miles, with the main like that.
I draw here what Antonio did. He is a good sailor.
Hope it helps someone in the future.
Remeber you need to release the foot on batten sails so they go up.
(If you don't like it go to McDonalds...their Whoper is on promotion this week.)