Always

use strict;
use warnings;
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It would have told you that $string_2 wasn't declared, and hence probably a mistake. It should be $string. Also, in your second regex, you probably want $next_word and not $string, and finally, $1, etc. get reset after each successful regex match. So you need to save them after each use. So:

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

my $string = " info
                  
                    John
                  
              
              
                
                100 - 2000
                
              
            
                
                  Kent";
my $word = "info";
$string =~ /$word\s*?(\S+)/;
my $next_word = $1;
$string =~ /$next_word\s*?(\S+)/;
my $next_word_2 = $1;
print "The next word after $word is $next_word\n";
print "The next word or number after $next_word is $next_word_2\n";
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