This may not solve your problem but as you are returning JSON you need to set that in the header, so instead of:

print "Content-type: text/html\n\n";
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Try:

print "Content-type: application/json\n\n";
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Also, you should really get the value of the query string by creating a new CGI object, so your script would be something like this:

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

my $cgi = CGI->new();
my $string = $cgi->param('s');
my $json = encode_json( [$string] );
print $cgi->header( -type => 'application/json' );
print $json;
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Update:
You probably need to modify your Javascript function too:

function perlExecute(term){
    $.ajax({
        type: 'POST',
        url: '/cgi-bin/doma.pl',
        data: { 's': term },
        success: function(res) {
        alert(res);
        },
        error: function() {alert("did not work");}
    });
};
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