You've received some excellent advice about your code. At the risk of confusing the issue (and I apologize in advance if it does), consider the following:

use Modern::Perl;
use open ':utf8';
use autodie;

my (%nonmatchhash, @hashvalues);

open my $NONMATCHINPUT, '<', 'OutputNonMatchedWords.txt';

do { /(.*)\t(.*)/; $nonmatchhash{$1} = $2; push @hashvalues, $2 }
  for <$NONMATCHINPUT>;

close $NONMATCHINPUT;

while ( my ( $key, $value ) = each %nonmatchhash ) {

    given ($key) {
        when (/\A$value\z/) {
            say "key '$key' eq value '$value'";
        }

        when (/(.*)(agtig)(e|er|ste)?$/) {
            say "$key\t$_" 
              for grep /(.*)(achtig)(e|er|ste)?$/, @hashvalues;
        }

        default {
            say "No match for key '$key'";
        }
    }
}
[download]

From what I could gather from your code, it looks like you're taking an action after testing for three conditions, viz., 1) key/value equality, 2) matching a key, then a value under that key, and 3) no match. The script above handles these three cases, and may assist your coding decisions.

Hope this helps!