You can use an alternative with the $1 in the first branch - it will be tried first.

#!/usr/bin/perl
use strict;
use feature qw{ say };
use warnings;

for my $line ('<div id="roguebin-response-35911" class="bin-response">
+</div>',
              '<div id="roguebin-response-35911" class="bin-response">
+'
) {
    if ($line =~ m{<div.+(</div)|<div.+}) {
        say "line matched";
        if (defined $1) {
            say "right after match, 1 is defined: $1";
        }
    }
}
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