Background
About six months ago we had sign-off for the completion of a software project with an external client and the remaining budget for that project was filtered back into other projects. I was revisiting the project to refine the documentation when I realised a non-critical part of the software wouldn't behave as intended. A single unit test would not change a value correctly, causing the test to always pass even if the system would change in such a way to make it fail. I was unsure how to handle this situation as the project has officially ended and we are no longer receiving funding to work on it. The faulty test doesn't stop the software from working as intended.
Fixing the issue would be trivial enough, but to have it deployed on the customer's system would require a lengthy process to be triggered which would involve much more work than just making the fix.
Question
In general, what is the best way to handle this sort of situation? I know the answer from management will be to just leave it, but I feel like just leaving it without letting anybody know would be the wrong thing to do. On the other hand, I feel like letting management know about this would be seen as time wasting, especially since we're no longer being paid to work on this project and it's such an inconsequential issue.
Edits
With regards to Erik's answer:
We have a ticketing system where support requests and change requests are filtered out. Support requests are handled and change requests are put into a different system. The issue I see with this is that the project was signed off and accepted by the customer after testing and they do not have a support agreement with our company.
A single unit test would not change a value correctly, causing the test to always pass even if the system would change in such a way to make it fail.
Is it the unit test that is defective or the system that is? – Y12K Oct 12 '17 at 9:36