In a nutshell, here's what's happening. Every computer running Adobe's Flash (and Flash runs on more computers than even Windows!) has an area set aside where websites can store and retrieve information. The Local Shared Objects, as they're called, persist across Web sessions, just like regular cookies. Unlike regular cookies, LSOs have no set expiration date, and they aren't controlled by any browser settings. You may configure browsers in your company to reject cookies, or reject third party cookies, but those settings don't do diddly with Flash LSOs.
Zombie cookies come into play with savvy websites that set a cookie, but then set a similar backup cookie in the Flash LSO area. When the browser returns to the site (or a site with content hosted on another site), the site looks to see if there's a cookie, in the usual way. If there isn't any, the site looks in the Flash LSO area, and re-constitutes the cookie if it can. Thus, even if your policies wipe out cookies during a session, or at the end of a session, the Flash LSO data can help the site bring the cookie back from the dead.
You might assume that Adobe, once it learned that Flash had been subverted to undermine user and corporate cookie settings, would've sprung to Flash's defense, unleashing a flood of publicity and tools to allow individuals and companies to control Flash LSO data. Not so. All we Flash users received was a finger-wagging position statement (PDF), sent to the U.S. Federal Trade Commission:
"Adobe condemns the practice of using Local Storage to back up browser cookies for the purpose of restoring them later without user knowledge and express consent. "
Blocking Flash cookies is not straightforward. LSOs are stored in files with extension .SOL. On most Windows PCs, they're in folders under %APPDATA%\Macromedia\Flash Player\#SharedObjects\ and %APPDATA%\Macromedia\Flash Player\macromedia.com\support\flashplayer\sys.
The official method for cleaning and blocking Flash LSOs on an individual machine hasn't changed in more than two years. To block Flash cookies the official way, you have to go to Adobe's Flash Player Settings Manager site and adjust the settings in the image at the top of the page. (Hard to believe, but the graphic that looks like a screen shot is, in fact, the Settings Manager, and it changes the settings on the PC being used to view it.) To the best of my knowledge, Adobe hasn't seen fit to release a program or any other product that allows you to control Flash cookies. You have to visit this website, machine by machine.