This works:

$ perl -le'kill TTOU => 0 or die $!; print "done"'

[1]+  Stopped       perl -le'kill TTOU => 0 or die $!; print "done"'

$ fg
perl -le'kill TTOU => 0 or die $!; print "done"'
done
[download]

Check for an error. If there's no error, it's not a problem sending the signal aka not a Perl problem.