Let me describe a simple use-case:
Running all tests in our project may take up to 10 minutes.
Sometimes I see an obvious bug in my code after the first failed test, so I want to stop running all tests, fix the bug and re-run them. Unfortunately, I can either re-run all tests from the beginning, or re-run failed tests only.
Is there a plugin for IDEA which allows me to re-run failed tests AND tests, which weren't yet executed when I pressed "STOP"?
This goes against the idea of a test suite. Normally you want to run all your tests specifically so you know you haven't broken anything somewhere unexpected. If you change the code and then run a subset of the tests, the possibility exists that you broke something and one of the skipped tests would have failed. This is a case of not getting your cake and eating it too.
If you find a bug in an early test, by all means stop the suite. Fix the bug but then run the suite from the beginning.
Atlassian has the solution for your problem: Clover. But it is commercial.