Unless you want special handling for the large invoices, it looks like your code is already doing that. Consider the following mutation of your code for demonstration purposes:

use warnings;
use strict;

my $chunksize = 50;
my $filenumber = 0;
my $outsize = $chunksize + 1;
my $eof = 0;

while (<DATA>) {
    if ($outsize > $chunksize and /^11/) {
        $outsize = 0;
        $filenumber++;
        print "*** New file number $filenumber\n";
    }

    print "$_";
    $outsize += length;
}

__DATA__
11 The first invoice.
We get this whole thing even though it exceeds the 50 character limit
because the conditional code requires an invoice marker before it will
start a new file.
11 Second
11 Third
11 Fourth invoice
11 Fifth invoice
This one is longer, but not excessive
11 Sixth: break before because limit hit in fifth
11 seventh and final
[download]

Prints:

*** New file number 1
11 The first invoice.
We get this whole thing even though it exceeds the 50 character limit
because the conditional code requires an invoice marker before it will
start a new file.
*** New file number 2
11 Second
11 Third
11 Fourth invoice
11 Fifth invoice
This one is longer, but not excessive
*** New file number 3
11 Sixth: break before because limit hit in fifth
11 seventh and final
[download]

How would the output be different to achieve what you want?

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