Your command points stdin to the output of some random command. Even if you actually redirected stdout (pipe to cat, not from), it still wouldn't work, because cat's stdin isn't a file.

You need to point stdout to an actual file, like this:

    shred > /my/secret/file.txt

Why would you do this? At the end of a long batch of commands that all write to some temporary file opened on stdout. Not uncommon in shell-land.