With property based testing, it actually CAN be 9 passes and 1 failure, because that one single fail can be hitting an edge case the others just aren't. In fact, only a few failures are more likely than it being all failures
I can tell you from experience that random failures cause loss of trust. People learn to ignore failures and just keep hitting rebuild until the tests pass. People will not investigate test failures in code that they don't understand.
But yeah, probabilistic testing isn't perfect.
Allowing reproducibility for a given change set.
Didn't even enter my mind.
Hypothesis has a nice option, to pick the seed for each property by hashing that property's code. It's a nice idea, but relies on Python's highly dynamic nature; so may not be easy/possible in other languages (especially compiled ones).
The co-worker should add the test to a new branch / test it on main. If it fails that's a new ticket (with the great side effect of having a failing test). If that passes it's a problem in their branch. If not it's the same as having a broken main which happens anyway and you deal with that as you usually do.
You can have a prng seeded from something like the commit hash and have prngs generate the test cases. That still can fail on 1/10 tests for a particular run.
The most memorable discussion I had around PBT was with a colleague (a skip report) who saw "true" randomness as a net benefit and that reproducibility was not a critical characteristic of the test suite (I guess the reasoning was then it could catch things at a later date?). To be honest, it scared the hell out of me and I pushed back pretty hard on them and the broader team.
I have no issue with a psuedo-random set of test cases that are declaratively generated. That makes sense if that is what is meant by PBT. Since it is just a more efficient way of testing (and you would assume this would allow you to cast a wider net).
The idea is you have random testing and the test failures are added as explicit tests that then always get run.
Is that so different from someone else testing?
The main issue is you stumble across a new issue in an unrelated branch, but it's not wildly different from doing that while using your application.