Idea 1: For a task/sub-task - there could be a button, "Request Update". When pressed, the assignee gets a notification asking them to update their task status/add comment.
Idea 2: A general button, "Request Updates", when pressed will send a status update request to all people whose tasks are being displayed. Even better, the email would contain links to all the tasks that I'm interested in.
E.g. In Project/List view - I filter the tasks by a particular person (A), and for everything that is overdue. The large list shrinks to 5 tasks. I press the update button, and an email is generated to person (A) with hyperlinks to the 5 tasks.