Given that the input file has a very large number of lines, I would try to just process the file line by line (no slurping the file into a single $file_content or @lines).

Here is one way:

#/usr/bin/perl -w
use strict;

my $cur_num;
while (<DATA>)
{
   $cur_num = $1 if (/^(\d+)/); # new $cur num if line starts 
                                # with digits
   s/(\S+)$/$cur_num/; # substitute the non-spaces at the end 
                       # of the line with the cur_num
   print;      #a blank line is not modified
}

=Prints
0       0
        0
        0

13      13
        13

28      28
        28

42      42
        42
        42

55      55
        55
        55
        55
=cut

__DATA__
0       ASDF
        ASEE
        ASEE

13      DERG
        DREG

28      QWER
        QWER

42      WERT
        WERT
        WERT

55      QWEASD
        QWEASD
        QWEASD
        QWEASD
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