Good use of //. Confirmed that it works:

use strict;
use warnings;

my $fh = \*DATA;

while (! eof $fh) {
    my @lines = map { <$fh> // () } 1..10;
    print "lines = " . @lines . "\n";
}

__DATA__
line 1
line 2
line 3
line 4
line 5
line 6
line 7
line 8
line 9
line 10
line 11
line 12
line 13
line 14
line 15
line 16
line 17
[download]

Outputs:

lines = 10
lines = 7
[download]