my ($a,$b);
while( $a=<F1>, $b= <F2>, $a or $b) {
  ...
}
[download]

reads till the end of the longer file. Changing to and limits to shorter one.

UPDATE Please note

Since $a and $b are not chomped, no normal input line should ever be false and hence not necessarily tested with defined.

Better take care if you are using special filehandles allowed to return a simple 0 or null strings!!!

UPDATE

safer:

use strict;
use warnings;
use Data::Dump qw/pp/;

open my $f1, "<", \ join "\n", 1..2;
open my $f2, "<", \ join "\n", 1..5;

while( defined (my $a=<$f1>) + defined (my $b=<$f2>) ) {
  $a .="";
  $b .="";
  chomp($a,$b);
  print "$a,$b\n";
}
[download]

1,1
2,2
,3
,4
,5
[download]

In boolean context: + is like or, * is like and, just w/o short circuit.