windows - How do you free up a port being held open by dead process?

A colleague of mine recently ran into a problem where a process that had supposedly died was still bound to a network port, preventing other processes from binding to that port. Specifically, netstat -a -b was reporting that a process named System with PID 4476 had port 60001 open, except no process with PID 4476 existed, at least as far as I could tell.

Process Explorer and Task Manager did not list PID 4476 (though there was another process named System with PID 4, which had its own set of TCP connections that did not include 60001). taskkill /PID 4476 also reported that PID 4476 could not be found.

Is there a way to kill this mysterious System process to free up the port to which it's currently bound? What can cause this to happen? How can there be processes that none of Task Manager, Process Explorer, and taskkill don't know about? Rebooting managed to fix the problem, but I'd like to know if there's a way to fix this without rebooting.