We tell the children and we tell the children: use strict; use warnings;. In this case turning on warnings generates a whole bunch of

Use of uninitialized value in concatenation (.) or string at noname1.p
+l line 23.
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warnings. A clue perhaps? Indeed, an unsubtle clue! A hit you about the ears and do something clue. First thing to notice is that all the warnings are in trim_end, so remove trim_start and try again - same result. Ok, remove some cruft and the code looks like:

use strict;
use warnings;
my $test = 'abc , def';

$test =~ /([\s\w]+),([\s\w]+)/;
for ($1, $2) {
    my $string = $_;

    $string =~ s/\s+\z//ms;
    print "$string\n";
}
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and generates (omitting the warnings):

abc
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Now look at what the code does. It performs a regular expression match setting $1 and $2. It then (in the loop) performs two more matches where the first fails and the second sees an undefined value. At this point it is worth noting from perlre that:

The numbered match variables ($1, $2, $3, etc.) and the related punctuation set ($+, $&, $`, $', and $^N) are all dynamically scoped until the end of the enclosing block or until the next successful match, whichever comes first.

but the first match in the loop is successful so $2 goes out of scope - becomes undefined. Capeesh?

Remember: use those strictures.