Canceling the draping doesn't stop the explosion. 
Even changing back to the Pose room doesn't stop the geometry from exploding into infinity.  A few seconds later, total app crash.

The same thing happened a couple days ago, it was her hand that exploded.

I did not have it that drastic. When I had exploding polys in a cloth sim, it were always intersections with the model before the simulation starts. May that be the case here too?

What exactly is going crazy?  Looking at your pic I'm not even sure the problem is with any dynamic cloth (which would seem to be the skirt, in your scene).

Maybe the first 2 simulations didn't totally clear?

When I first did the dynamic simulation, before saving the skirt to the library,
I posed her in frame 20.
This time the pose is in frame 1.

The top menu has the thing to re-do all cloth and all hair. 
Should I be using that instead of going back to the Cloth room?
Should I be turning off the 'drape from zero pose'?

It worked so nicely the first go round.   It's frustrating.

Ah you're trying to treat that hair as dynamic?  Good luck with that, I'm surprised you got it to complete even once.

It's clear from the picture that you've got intersections between the hair and the figure's ears.
The cloth simulator is pretty much guaranteed to blow up.

I was simulating the SKIRT!  Not the hair      are you teasing me? :huh:

anyhoo, saving dynamic clothes to the library is futile.

my stein is empty.

I'm sorry, I got the idea that you had set the hair up as dynamic.  If the skirt is the only object that has been Clothified, then I think your problem is one of two things:

1. There may be some geometry for the skirt that is actually inside the character's body, or intersecting itself, and is getting squirted out of the head eventually through bad luck;
2. You have a bugged version of V4 and need to download the updated version, install it, and run the "Update V4" script.