Ben Gurion Airport is now closed for incoming and outgoing commercial flights.
It is possible to request permission to leave Israel for emergencies, see the application here. However, as above, there are no commercial flights. Hence, anyone who receives permission will need to travel by private plane.
Similarly, those seeking to enter Israel under extraordinary circumstances, will need to travel by private plane. Niftarim will only be able to arrive in Israel via private aircraft, or on cargo flights.
At present, the land crossings between Israel and Jordan and Egypt remain open. Some passengers are actually traveling to/from Israel via Amman and Cairo. However, Chaim V’Chessed has learned that authorities are considering closing these crossings in the near future.