So what's the purpose of $found?

If all you need is to find out if this line matches criteria and do something based on that, that's pretty well what "if" statements are for...

foreach $1 (sort keys %file1){
    foreach my $position1 (@{$file1{$1}}){
        foreach $contig_id(sort keys %hash_1){
            foreach my $position (@{$hash_1{$contig_id}}){
                if($1 =~ /^$contig_id/ && $contig_id=~ /^$1/ && $posit
+ion1==$position) {
                    print RESULTS "$position1\t$1\n";
                }
                else {
                    print "not matched\n";
                }
            }
        }
    }
}
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