Il bit setuid fa sì che il programma venga sempre eseguito con i permessi dell'utente proprietario. Tuttavia solo utenti privilegiati possono cambiare il proprietario di un file, e se non sono superuser i bit setuid e setgid vengono automaticamente disattivati.
Estratto da man 2 chown
Only a privileged process (Linux: one with the CAP_CHOWN capability)
may change the owner of a file. The owner of a file may change the
group of the file to any group of which that owner is a member. A
privileged process (Linux: with CAP_CHOWN) may change the group arbi‐
trarily.

If the owner or group is specified as -1, then that ID is not changed.

When the owner or group of an executable file are changed by a non-
superuser, the S_ISUID and S_ISGID mode bits are cleared. POSIX does
not specify whether this also should happen when root does the chown();
the Linux behavior depends on the kernel version. In case of a non-
group-executable file (i.e., one for which the S_IXGRP bit is not set)
the S_ISGID bit indicates mandatory locking, and is not cleared by a
chown().
Ovviamente un utente non privilegiato non può attivare i bit setuid e setgid di un file che ha come proprietario root, poiché i permessi possono essere cambiati solo dal proprietario del file.
Estratto da man 2 chmod
The effective UID of the calling process must match the owner of the
file, or the process must be privileged (Linux: it must have the
CAP_FOWNER capability).