OK! Now I'm seeing the bigger picture.
The "sheet" you were describing is the sail! You should be aware that in sailing terms a
sheet is a line (or in laymen's terms, a rope). We have jib sheets and main sheets that we adjust to set the position of the sails.
You may not necessarily have a problem with the halyard stretching because even if your halyard stretches, it should not jam. The halyard can stretch a foot on the front side of the mast, without affecting the location of the shackle during a full hoist. If the bolt rope on the sail had excessive stretch, then the shackle might be pulled to the sheave. But that also isn't likely because bolt ropes usually shrink, which makes it increasingly difficult to get a full hoist.
Your problem may be related to a mainsail that has been cut too long in the luff. Or, perhaps, the previous owner raised the position of the boom a few inches, so that a sail that once fit properly, is now raised too high.
It's also feasible that there is a problem with the sheave. You'll figure it out soon enough!