Really? They have not taken another religion? Judaism, is centralized around the Torah, and the covanent with G-d to follow his laws. Therefore, anyone who does not follow the laws is still a Jew because they have been born into this eternal covanent. Now, many of the liberal Jewish movements stress that following the laws are not binding. Some schools of Christianity believe the Torah to be the literal word of G-d, while Reform/Liberal Judaism says it may be divine, but belief it is from G-d is not required, nor is belief in G-d requred! If you did not know, the Talmud states believing in many gods (trinity) is better then belief in no G-d.
I am not sure if you understand that Judaism is much more then a religion of beliefs. The best explanantion I can show you is a very good one I read: Judaism maintains that one born Jewish or one who has converted to Judaism retains his or her status as a Jew forever. One who converts to another religion or is an atheist is considered to be a Jew not in good religious standing. How religious one is, in this sense, is only important in one's status in Jewish law. For example, a person denying the Jewish principles of faith may be considered a heretic, while still considered Jewish.
You can still be Jewish and be an apostate Jew. It is also worth noting that Reconstructionism does not require any belief in a deity, and that certain popular Reform prayer books such as Gates of Prayer offer some services without mention of Hashem.
Well I will try to find the answer for you though I doubt there is one single agreed upon halacha for a Jew who converts to Christianity who actually wants to be buried in a Jewish cemetery, since why be buried with the people who you believe are in for "eternal hell".