Trivial case: obviously irrelevant, surely? If you have no choice then you have no choice, and it doesn't really matter whether or not you estimate that it's worth continuing.

Not irrelevant from a prediction perspective.

If you observe a lot more apparently-unrelated slippages than you expected, then they aren't truly unrelated, in the following sense: you should start thinking it more likely that you did a poor job of predicting slippages (and perhaps that you just aren't very good at it for this project). That would lead you to increase your subsequent time estimates.

If this happens consistently in projects, yes. If 5% of your projects fall out of normal ranges for a 95% confidence interval probability distribution - then your estimates were good.

as with the "slightly less trivial" case but more so, I don't think this is actually an example, because once you start to suspect you're getting mugged your time estimates should increase dramatically.

That assumes you realize you are being mugged. As one example, we had a client (since fired) who added increasingly complex-to-calculate database fields as a project went on, with each set of new sample files (they were developing a system concurrently with ours to process our output, and was basically dumping the stuff they didn't want to do on us). We caught on that we were getting mugged when they deleted and renamed some columns; until then, we operated on the assumption of good faith, but the project just never went anywhere.