If you're asking this question, then it sounds like your assignor has the "Availability Locking" feature turned on. If this is the case, then you are not permitted to change your availability once you've received an assignment. Only your assignor can change your availability at that point. The "Availability Locking" feature is an optional feature that your assignor can turn on or off as they desire so you would need to contact them to inquire about their specific assigning practices.
You can read more about the Availability Locking feature at this support article.