said by TomS_:
Breakout box" is probably not the right term, but its the best thing I can think of to describe it right now. The page above suggests "lead in module" but Im not experienced enough with PON to know if thats an industry standard term, or just what the operator of that PON network is calling it.
The box in the handhole is a Corning OptiSheath multiport terminal, its purpose is to serve as a handoff where an SC to X drop cable can be connected to a fiber F2.
The lead-in is a fiber stub that is fusion spliced into the cable pairs and can be ordered in lengths as needed to meet the buried fiber run.