Looking at the relevant part of POE::Wheel::Run, it looks like the following:

    # $program is what you pass in as the Program key
    # $progargs is the array reference of arguments
    else {
      if (ref($program) eq 'ARRAY') {
        exec(@$program, @$prog_args)
          or die "can't exec (@$program) in child pid $$: $!";
      }
      else {
        exec(join(" ", $program, @$prog_args))
          or die "can't exec ($program) in child pid $$: $!";
      }
    }
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So basically, your program gets run as one string, so you need to either supply the shell-safe quoting yourself (not so good idea) or avoid the shell alltogether by passing Program and ProgramArgs as array references (very good idea):

my $wheel = POE::Wheel::Run->new(
  Program => [ $program ],             # changed!
  ProgramArgs => \@progargs,

  StdinEvent => 'stdin',
  StderrEvent => 'stderr',
  StdoutEvent => "stdout",     
  StdoutFilter => POE::Filter::Stream->new(),
 );
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should work, or the worse solution is to quote the program arguments twice:

$progargs = (q{"SELECT * FROM MY_TABLE;"});
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See perlop for more about the q{} operator.