Here we are covering on how toprevent changing root password from single user mode?

open file “/etc/rc1.d/S99single” in your favourite editor and search for line.

exec init -t1 s

Just add the following line above it. save it an exit.

exec sbin/sulogin
Now before entering single user mode you will need to provide root password to proceed. Check again trying to enter single user mode after these changing above said file.