The code I was using as recreated below was correct:
jQuery('select#edit-field-status-0-field-status-und').val(1).change();
I found out the reason why it wasn't working was because the ID of the target element changed dynamically. So when I first inspected and found edit-field-status-0-field-status-und, the same element would change IDs to something like edit-field-status-0-field-status-und--1.
That was throwing things off and gave the impression my code wasn't working.
Thanks to @gts for your input.