Maybe the wrong quotation marks?
<script type="text/javascript">
jQuery(document).ready(function() {
jQuery('#send_message_form').submit( function() {
jQuery('#subject').val("Some message subject");
});
});
</script>
Unfortunately I’m not sure what the code is supposed to do – this is something you will need to check with BP’s support.
wp_footer
is a WordPress hook and usually is the place to add custom js code.
Execute PHP does not need to be checked.