We've adopted a fairly arbitrary rule that all pull requests have to improve test coverage, even if the code you are submitting is already 100% covered. It's simply a matter of forcing everyone to take care of low-hanging fruit in terms of untested code that's been sitting around for a while.
I'm not always a fan of strict arbitrary rules. It's a bit silly if I think about it too hard, but so far I'm really enjoying it. It forces us to make our code more testable if we don't want this constraint to be too tedious. It also makes us quicker to remove dead code because it's a quick way to improve test coverage.