I doubt pull requests with failing tests for bugs are ever going to be that common (unless you have a really good testing department between you and the end use

I doubt pull requests with failing tests for bugs are ever going to be that common (unless you have a really good testing department between you and the end user capable of writing the tests) but if they did then the correct way of dealing with them would be to identify the bug, correct the problem in the source and create / modify the test so that your test covers the general failure mode.