Really depends on the failure.
Uninstalling Office through normal means should clear out traces of Office in the registry, particularly the keys that BigFix patch content checks against. Third party tools or in-house scripts used to “force” an uninstall, perhaps maybe because normal means of removing Office were not working, could leave behind keys, but this means the system was in a bad state to begin with.
Common exit codes with failed Office patches are 17025, 17028, and 17029.
Generally, 17029 errors are due to problems with the Office installation and can also affect detection by Microsoft’s native detection tools, Microsoft Updates and the now deprecated MBSA tool. Again, if you have third party tools or in-house scripts that are doing “performance” or “cleanup” on the system, it’s possible those tools removed something they shouldn’t have.
With 17028 errors, it could kind of go both ways. If these were preceded with 17029 errors, then there could still be lingering issues from the 17029 problem, ie: left over keys. But this could also be an issue with the patch content.
With 17025 errors, I’d say this could be an issue with the patch content.
Everything mentioned above is a generalization. Really depends on your specific scenario and environment history.