Leo Fender's original design, including foam rubber glued to the underside of the bridge cover to damp the strings, was to try to emulate double bass in a more portable and stable format, with the fretted neck giving the instrument its characteristic intonation, and thus the "Precision" name.Is the tone of an electric bass closer to a double bass or cello?
Then someone took off the bridge cover, or perhaps forgot or decided not to put it back on when restringing, or the foam rubber deteriorated, and noticed a lot more sustain. Add some natural overdrive and compression from diming a smaller tube bass amp, and you start getting the "cello-like" sustain that all the lead guitar players strive for.