defect classification

After finding and reporting a bug, a tester may get this response from a developer: "Please rerun the test on the latest version of the code and check if the bug still reproduces." This seems like a rational request; just as a change can cause a bug to appear, it can also fix a bug. But is following up the responsibility of the tester or the developer? And if the bug is no longer there, how do you classify and close it?