Not really sure what you're asking. When you execute programs, they run as you. You can su them to run as another user, but you have to become the other user first (ie you have to know their password).
I think the scenario you are describing is that a file is created by the user victim with the following permissions:
-rwxrwxrwx 1 victim victim exec_file
and you want user to be able to execute the file and have it run as victim.
victim could use setuid to set the special bit of the executable like this:
victim$ chmod u+s exec_file
victim$ ls
-rwsrwxrwx 1 victim victim exec_file
Now when user runs the file, it will run as victim. This is not a vulnerability or an attack since victim explicitly set it up this way.
You might think that the following would work:
user$ ls
-rwxrwxrwx 1 user user exec_file
user$ chmod u+s exec_file
user$ chown victim exec_file
user$ ./execfile # I'm victim now, right?
but linux will prevent you from doing the chown unless you sudo it, ... but if you have sudo powers already, then this isn't really much of an attack.
The closest thing I can think of to making this an actual attack is if multiple users run this program on a regular basis, and you have write permissions on it, then you can replace it with your own code and wait for the owner (or anybody else) to come back and run it. Now somebody else is running your malicious code as themself. In general, bad idea to give users write permission over files that other users will execute. Far better to have it like this:
-rwxr-xr-x 1 user user exec_file
or even better:
-rwxr-xr-x 1 root root exec_file