You can consider that peu s’en faut is a fixed phrase that deviates from the standard syntax rules (I have the feeling it is actually an archaic turn but cannot find any evidence to back this up).

Same eg for tant s’en faut or point trop n’en faut.

Peu s’en faut means that something almost happened. That is also the meaning in the exceprt you are refering too, from "La Vie de Galilée": it means "he’s almost dead", "he is virtually dead".

EDIT: this article (thank you Dimitris) confirms that the omission of the impersonal il is an archaic turn.