Actually, H4 is a type of visa for dependents of H-1 or H-1B visa holders.
Typically, dependents of H-1 or H-1B visa holders cannot work and have perceived need for a SSN, so no SSN is issued.
However, they DO need a tax ID number if they are to be included on the sponsor's tax return, so the IRS issues ITINs. These ITINs are issued when Form W-7 is submitted (with proper identification documents) along with the annual tax return.
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