… the target user's UID. It allocates a new PTY for that, and then shovels data back and forth from the originating TTY and this PTY.
Or in other words: the target command is invoked in an isolated exec context, freshly forked off PID 1, without inheriting any context from the client (well, admittedly, we *do* propagate $TERM, but that's an explicit exception, i.e. allowlist rather than denylist).
One could say, "run0" is closer to behaviour of "ssh" than to "sudo", in many ways. Except that…