I'm Philippines passport holder and currently living in Israel. A few months ago my resident permit expired and I'm ready to go back home for good. My question is - can I apply for a Schengen visa in Greece even for just 2 weeks because I want to travel before going back to the Philippines?
You will need a valid resident/work visa in the host country in order to apply for a Schengen Visa (in a foreign country).
I could not find a specific page for your case (Greek Embassy in Israel) but going quickly through few other Greek Embassies in other countries (for example, the Greek embassy in the U.S website) shows that a Valid resident visa is required, hence I am sure all other Greek embassies will ask for the same.