What is the function of the oil pressure sending unit behind the oil filter? What happens if it doesent work or the wire to the unit becomes disconnected?

I believe it is only connected to the oil light in your dash, so, nothing really. :)

Yep, just looked it up, according to my FSM, the '91 Sentra SE-R/NX 2000 (and probably all b13s), are that awy.