I've not heard of that before, Does it only affect Firefox, or does this instance of iexplore.exe that is still running prevent any other applications from running?
What I would do. I would try and find out why IE is not closing down properly, and the experience with IE is that often bad Add-ons, 3rd party toolbars or ActiveX components are the culprit.
Try IE in it's Safe Mode, eg go to the Start bubble > All Programs > Accessories > System Tools > Internet Explorer (No Add-Ons), and click.
This IE opens with all 3rd party add-ons disabled. It should still surf the internet, but since many web sites now use additional components to enhance their web pages, many pages won't render properly. However, the test is, close down IE, then try to open Firefox. If that works and if there are no instances of iexplore.exe in the Task Manager, then you can start looking at IE's Add-ons, (IE > Tools > Manage add-ons).
Hope that helps.
Mark
I am using WIN7. Even after shutting down IE8, I note iexplore still remains in task manager. I attempt to click on Firefox icon on desktop. Firefox is unresponsive until I delete the iexplore remnant from task manager. Help.

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