Estimating "structural integrity" of simple voxel-based objects?

Heyo! Hit an imposing wall while feature-planning. Will dance for advice.

Let's ignore all other concerns as extraneous. Imagine an isolated voxel creation of modest complexity - no more than 4096 cells. Boom! A drunken tyrannosaurus stumbles into it. (He'll be fine.) Grab a brush selection around the hitpoint and damage these voxels. Let's say some are removed. I then have three possible outcomes:

• The resulting shape maintains its overall appearance of integrity.
• The resulting shapes are isolated by negative space.
• The resulting shape(s) include features which appear to be hanging by a thread.

In the latter case, I'd like to isolate these stressed voxels for removal, ultimately bumping the situation back to case 2. Given unlimited CPU time I could maybe hack something together, but even then I doubt I could write an industry-grade solution. I'm pretty clueless about how to approach the problem.

Makes me think there's a good reason I can't recall ever seeing this tech before. If anyone has any advice for me, I'd really appreciate it!