When you have the Erasure Quality, does whatever agent (hacker, AI...) that routinely wipes off any infor about the character in the Matrix, destroy also Fake SINs after a while, or are they left alone ? The rather dreary perspective of living truly SINless, wthout even Fake SINs to rely on, leaves me questioning the value of this Quality.

Going by the book, the preserver will leave SINs and data "alive" if the character wishes (and the benefactor knows it).