A parser which consumes the string would be an example application.

Then It would be better to test for the success of the operation that consumes the string, than perform that operation and then test to see if there is any string left to consume. Simplistically:

cmpthese -1, { 
    a=>q[ 1 while chop( $sa )         ], 
    b=>q[ chop( $sb ) while $sb ne '' ] 
};;
        Rate    b    a
b  8537447/s   -- -59%
a 20591583/s 141%   --
[download]

But most other operations that alter (reduce) the length of a scalar can be tested in the same way.

That said, if there is any reason why the reducing operation itself cannot be used as the controlling condition, just testing the string for truth achieves the desired effect even more efficiently:

[0] Perl> cmpthese -1, { 
     a=>q[ 1 while chop( $sa )         ], 
     b=>q[ chop( $sb ) while $sb ne '' ], 
     c=>q[ chop( $sc ) while $sc       ] 
};;
        Rate    b    a    c
b  8686428/s   --  -2% -20%
a  8821000/s   2%   -- -19%
c 10841356/s  25%  23%   --
[download]

Though I realise that can fail under some conditions.