This might answer your question.....

https://www.nafsa.org/uploadedFiles/Chez_NAFSA/Find_Resources/Supporting_International_Students_And_Scholars/ISS_Issues/USCIS%20FAQ%20Statelessness%20and%20the%20Ability%20to%20Work%20for%20Joint%20F1%20TPS.pdf


SIRAK,
YOu can attend college in H4 status and few other status. Doesn't have to be in F-1.