#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say };
use List::Util qw{ shuffle };

my @words = qw( this is a string with a word );
my @order = 0 .. $#words;

my %ord;
push @{ $ord{ $words[$_] } }, $_ for 0 .. $#words;  # <-- Here...

@words = shuffle(@words);
@order = @ord{@words};

print do { local $" = "\t"; "@words\n" };
say join "\t", map "[@$_]", @order;

@order = map shift @$_, @order;                     # <-- and here.
say join ' ',
    map $words[$_],
    sort { $order[$a] <=> $order[$b] }
    @order;