When a custom field is configured as "required on update", the behaviour when going through bug_change_status_page, to change status, is to show all such required custom fields, and ensure they are not empty when submitting the changes.
However, when the "assign" action is used, and status is changed as a result (eg, by option auto_set_status_to_assigned), those required custom fields are not verified.

A proposal is:
When the assign action is performed through bug_update page, check:

• if the action results in a status change
• and custom fields exist with "required on update" option
• (and possibly) any of those custom fields are currently empty
  Then redirect to bug_change_status_page with the corresponding properties prefilled (new status, assignee)