A Fiber Termination Unit (FTU) is a small box that is attached to the side of a house that will act as the transition point from the backbone fiber network to the inside wiring. The box contains one or more fiber connectors and slack storage space for excess fiber. The drop fiber cable comes into the box and is spliced onto a connector pigtail. Some FTUs will have a reel of blowable fiber cable already connectorized, ready to be blown to the street connection point.
To extend the fiber into the house, you typically would use bend insensitive fiber cable - ie. fiber cable that can withstand much tighter radius bends. This cable has higher optical loss than backbone fiber, and costs more per foot, but the distance is so short that it doesn't matter. The inside cable would have connectors on both ends for connecting to the FTU and to the inside router.
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