Your regex is obviously not working properly, because it prints beyond the boundary of 50 characters. Here's another option:

use strict;
use warnings;

my $string = "I'm trying to have a word wrapping using a regex in Perl
+. What I would like is about every 50 characters  or so to check for 
+the next white-space occurrence and replace that space with a newline
+, and then do this for the whole string.  I'd like to avoid looping o
+ne character at a time or using substr or placing the value into an a
+rray if possible. The code sample I have works, I'd like someone opti
+on and suggestion is there a better way or better regular expression 
+to accomplish this.";

print '1234567890'x5 . "\n";
print wrap($string, 50) . "\n";

sub wrap {
    my ($s, $wrap) = @_;
    my (@lines, $line);
    
    while (length $s > $wrap) {
        ### Take one extra character so we can see if
        ### we're wrapping inside a word or not
        $line = substr($s, 0, $wrap+1);
        $line =~ s/\s+(\S*)$//;
        push @lines, $line;

        ### Add any word fragments back on
        $s = $1 . substr($s, $wrap);
        $s =~ s/^\s+//;
    }
    return join "\n", @lines;
}
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