A detached thread must return, and I'm guessing on your platform, the socket isn't closing itself automatically. Maybe try something like this:

sub do_stuff {
   my $sock = shift;
   print "Client connected\n";

   while( my $input = <$sock> ) {
      chomp( $input );
      print "$input\n";
   }

   print "Client disconnected\n";

   $sock->close;
  #or
   close($sock);

return;

}
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