Unlike Fannie Mae and Freddie Mac securities (which are issued by the two GSEs), Ginnie Maes are issued by hundreds of individual firms. Quicken is an issuer; so is Wells Fargo. The loans inside of Ginnie Mae are all explicitly guaranteed by the US Government--they are all FHA, VA, or rural housing loans.
Also unlike FF, Ginnie does not guarantee securities; it guarantees the issuers of securities. If an issuer fails to meet its obligations to make principal and interest payments, Ginnie Mae takes them over, much like FDIC takes over a failed bank. When a loan within a security goes into default, the issuer is obligated the pull the loan out of the Ginnie Mae pool and pay the investors the principal balance at the point--from the standpoint of the investors, the default becomes a prepayment event.
So now the issuer has basically fronted a loan to the government: the issuer pays the security holder, and then is reimbursed for that payment when FHA/VA/Rural Housing pay a claim. Issuers should hold sufficient capital (or have sufficient lines of credit) to float the money to the government. But an event like Harvey could produce a big problem--lots of houses that go into foreclosure might never become conveyable, and so never get a mortgage insurance claim fulfilled. For issuers with concentrated business in Texas and Florida, this could create enormous stress.
There are measures government could take to prevent this problem, such as providing zero cost loans to homeowners for reconstruction, particularly outside of designated flood areas. But the leadership necessary to solve this problem is now, well, nonexistent. There is no FHA Commissioner and no Ginnie Mae President. A Deputy Secretary (who is a very good candidate) has been nominated but not confirmed. There is nobody home now, when we most need somebody.
I hope I am worrying over nothing, but I kind of doubt it.