Some crude debugging would help. Check to see if the file exists before you stat it, and establish a default value: The uninitialized warning is generated because $new_max is not a number yet.

Here's how I'd do it:

  
#!/usr/bin/perl
use warnings;
use strict;
my $largestsize = 0;
my  $size;
my $file = "filelist";
 open (FILE, "$file") or die $!;
 while (<FILE>) {
      chomp;
      if ( -e $_ ) {
          $size = (stat($_))[7];
          if ($size > $largestsize) {
              $largestsize = $size;
          }
      }
}
print ("$largestsize \n");
[download]