I don't think anyone has mentioned changing the record/line delimiter yet which seems like a good approach for this problem especially if you have multiple records in a file. You asked about processing line by line. That's the default because the delimiter ($/) is a newline (\n) by default (usually, different systems and read modes affect this too). You could play around with this.

{
    local $/ = "<SUBEND"; # localize or this is a bad idea.
    my $count = 0;
    while (<YOUR_FILE_HANDLE>)
    {
        next unless /SUBBEGIN/; # Don't catch trailing empty stuff.
        print "\nRECORD ", ++$count, " -------------------------\n";
        print $_;
    }
}
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