Not sure how common this problem is, but I see this not uncommonly described.
Is it related to the caps' thinness or simply because they're old and have been dropped, etc? Can one post this pen safely?
What is the best method to detect subtle cracks?
If a cap has been "stabilized", what questions should I ask in regards to how it was done and what was used to stabilize it?
Thanks!

Cracks in Balance cap lips are very common. The cause is a combination of the lip's thinness and the steep taper of the barrel where the cap posts. Posting exerts a great deal of tensile stress on the cap lip.

All but one of my Balances have a crack in the cap lip of some sort or another (or had one and I got it fixed). They're common. If the crack is not large it can be contained well often by not posting and by being careful with the pen and cap.