In case we are about to delete the PID directory, we clear the Process
pointer. If someone still holds a reference to the PID directory (by
opening it), we still need to delete the process, but we can't delete
the directory, so we will keep it alive, but any operation on it will
fail by propogating the error to userspace about that the Process was
deleted and therefore there's no meaning to trying to do operations on
the directory.
Fixes#8576.