I'd approach this differently. Instead of playing with magic variables that make the code hard to read, try to describe the algorithm in a simple way:

#!/usr/bin/perl
use warnings;
use strict;

my $input = << "EOF";
foo\tbar\t\tbaz\tbooz\t\tqaaz\t\t\tabc
foo\t\tbar\tbaz\t\tbooz\tqaaz\tabc\t123
foo\t\tbar\t\tbaz\t\tbooz\tqaaz\t\tabc
EOF

open my $in, '<', \$input or die $!;

my @tab_counts;
while (<$in>) {
    my $i = 0;
    for my $tab_count (map length, /(\t+)/g) {
        $tab_counts[$i] = $tab_count if $tab_count > ($tab_counts[$i] 
+|| 0);
        ++$i;
    }
}
push @tab_counts, 0;  # No tab after the last field.

seek $in, 0, 0;
while (<$in>) {
    my $i = 0;
    print $_, "\t" x $tab_counts[$i++] for /\S+/g;
    print "\n";
}
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