So I'm wrestling with one of my students tonight, and I set him up in an American lock, and he's resisting, and his elbow comes up pretty high, and then the arm gives and I hear a sound like ripping velcro. I have heard this sound before When someone was resisting an american lock and was wondering what the sound is? My guess is that it's the fascia in-between the muscles ripping. His arm was a bit sore, but he seems to be ok.

Any Doctors who do jiujutsu, or any anatomically wise among us who could shed some light on this for me?

Exactly, fascia tearing sounds like velcro being pulled apart.

After the Fascia tears, what is the next thing to go?

The joint will seperate. And hopefully he is not interested in continuing after that.
Jake