The classic is say you know a root process will write a file called foo.lock in /run/lock, and you (a bad person) have write access to that directory. Then you make foo.lock a symlink to some file (/bin/init or /bin/sh or ld.so for example would be very inconvenient choices) and when the root process writes its lock it destroys that file.

Now obviously people these days generally know about that so hopefully don’t use predictable file names but that’s one way.