Dependent children over age 21 are no longer eligible for F-2 status and will need to change to another status, such as F-1 (for full-time students), if they wish to stay in the U.S.
At the end of the F-1 program, there is a 60-day grace period during which the F-1/F-2 may stay in the U.S. Once the F-1 primary leaves the U.S., the F-2 dependents must leave as well.
The F-2 spouse and children of an F-1 student may not accept employment in the U.S. However, they may do volunteer work as long as there is no compensation of any kind and the F-2 dependent is doing a job usually done by volunteers. For more information about policies on volunteer work, please read more here.
F-2 dependents of F-1 students in the United States may study part time at the postsecondary level in any certified program at an SEVP-certified school, as long as the study does not amount to what regulations define as full time for an F-1 student [defined in 8 CFR 214.2(f)(6)].
F-2 dependents may also study full time in avocational or recreational studies, such as hobbies. F-2 minor children must comply with compulsory education requirements in attending kindergarten through 12th grade. If you have questions on how the secondary school system functions in Austin, here is a video (Navigating the Austin School System: A Comprehensive Guide for Parents) that will give you an overview.
However, an F-2 dependent who wants to enroll full time in a course of postsecondary academic or vocational study must apply for and obtain approval to change nonimmigrant status to F-1, J-1, or M-1 before beginning their full-time study.