Update: simplified a bit more.

A bit simpler than the other suggestions, and it works.

use strict;

while( <DATA> ) {
    if( /^1$/ ) {
        my $n = 0;
        ++$n while defined( $_ = <DATA> ) and /^\n$/;
        $n = 1 if /_____ 2/;
        print '1', "\n" x $n;
    }
    print;
}
__DATA__


1


b

1



_____ 2
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There are two keys to the simplicity.

1. You don't have to only read lines at the top of the loop.
2. There is no need to buffer the newlines, just count them.