The Mishneh Berurah (448:11) writes that regarding chametz owned by a Jew over Pesach, from which one cannot benefit normally, if the chametz was sold to an apostate Jew because he is a friend and you know that he will return the chametz to you after Pesach, and you figured (in error) that an apostate Jew is for all matters considered to be a non-Jew, then b'dieved (after the fact) and in a case where there is a large financial loss possible, the Mishneh Berurah provides a way of benefiting from the chametz, by selling it or trading it and then benefiting from the profits or the exchange.
From this we see that for rabbinic prohibitions, there is some room for benefiting from the improper behavior of an apostate Jew, in cases of loss. Although the exact particulars of to apply this din will depend on individual circumstance (and from the Taz there #4 it appears that this might be limited to the case of chametz). But here too, the question is about benefiting from work done on Shabbos, which is also a rabbinic "fine" like benefiting from chametz.
The Sheilas David OH #5 writes that lifnei iver only applies to regular Jews or sinning Jews who might do tshuva, but not to a mumar (apostate Jew) who has no expectation of doing tshuva. For such a person, in a case of an issur d'rabanan, he writes that we can rely on the view that there is no problem of lifnei iver, because there never was a gezera of "aiding sinners" for such an apostate.
(Layman's summary: One cannot benefit from leavened food that was owned by a Jew during Passover. But according to some authorities, if the Jew in question was an apostate, then one can benefit from that leavened food. The reason is that the prohibition on benefiting was established as a fine to prevent people from sinning and keeping their leavened food, but an apostate is already sinning anyway, so the fine was never applied to such a person, and thus others can benefit from leavened food owned by the apostate. Extending this rule about Passover to other cases is not a simple matter, but may be possible)