Pulling out the threads usually happens when you have not engaged the puller into enough threads, or when there is a washer hiding at the bottom of the threads stopping the puller from pushing on the bottom bracket spindle. As above, if you remove the washer and try to use the remaining threads you will just rip them out too.

Do not ride without the bolt and wait for the cranks to remove themselves - this is liable to damage the square taper and ruin the cranks.

Go to a shop with a gear puller, or buy a gear puller yourself. They cost about $10 - $20. They have arms that can pull on the back of the crank instead of the threads. THe pin of the puller pushes on the threaded stud of the spindle (nutted spindle), or on a bolt partially inserted into the spindle (bolted spindle). Good luck!