The common term is "Feed through" GFI receptacle. It is designed with specific terminals to use for protecting other receptacles or devices. It is a very common device found in RV units, residential, and commercial properties. They often use feed through units to protect other receptacles. It is less costly to install just one feed through GFI and offers the same safety. It can be a bit less convenient for the user in that when the "main" feed through unit trips it de-energizes more than one receptacle.
Some information is in this early hit by doing the Google on the internets.
GFCI Outlet Wiring Methods
Posts happened while I was composing and, as always, slowly typing.
I agree with RodgerS that using parallel and series to describe a GFI feed through circuit is less than ideal.