What to do if I’m currently on H1 but my employer is asking me to file for Changes of Status from H1 to back H4 because he is not able to find a project for me?

The H-1B is a non-immigrant visa in the United States under the Immigration and Nationality Act, section 101(a)(15)(H). It allows US employers to temporarily employ foreign workers in specialty occupations. If a foreign worker in H-1B status quits or is dismissed from the sponsoring employer, the worker must either apply for and be granted a change of status to another non-immigrant status, find another employer (subject to application for adjustment of status and/or change of visa), or leave the US.

The regulations define a "specialty occupation" as requiring theoretical and practical application of a body of highly specialized knowledge in a field of human endeavor including but not limited to biotechnology, chemistry, architecture, engineering, mathematics, physical sciences, social sciences, medicine and health, education, law, accounting, business specialties, theology, and the arts, and requiring the attainment of a bachelor’s degree or its equivalent as a minimum (with the exception of fashion models, who must be "of distinguished merit and ability").Likewise, the foreign worker must possess at least a bachelor’s degree or its equivalent and state licensure, if required to practice in that field. H-1B work-authorization is strictly limited to employment by t

An H-4 visa is a visa issued by the U.S. Citizenship and Immigration Services (USCIS) to immediate family members (spouse and children under 21 years of age) of the H-1B visa holders.^[1]

USCIS allows immediate family members of H visa holders (H-1A, H-1B, H-2A, H-2B, or H-3) to get H-4 visas to lawfully come and stay in the US. These visas are usually issued at the local US consulate office abroad. However, if the person is already in US, he or she can obtain H-4 status by filing Form I-539 for change of status.^[2]

H-4 visa holders are not eligible to get a Social Security Number and cannot be employed, but they can hold a driver's license, open bank accounts, and get an Individual Taxpayer Identification Number for US tax purposes.

Family members may alternatively be admitted in other non-immigrant categories for which they qualify, such as the F-1 category for children or spouses who will be students or the H-1B category for a spouse whose employer has also obtained approval of an H-1B visa petition to employ the spouse. An H-4 visa holder is admitted to the US for the duration of the primary (H-1B, H-2A, H-2B, or H-3) visa validity.

Since H-4 visa holders are not issued a social security number, an ITIN (Individual tax identification number) should be obtained before filing for joint tax returns by filing Form W-7. They are not authorized to work in the United States, though they are allowed to study.  

I suggest that you consult further with an immigration attorney in your locality. One can be found in attorneypages.com. If you get an H4 visa you can remain in the country so long as the spinsoring relative has a valid H1 visa.