I have 2 elderly parents who are not well. If they need assistance they usually call me as I live the closes(10 walking blocks). 3 questions with Pikuach Nefesh in mind: 1) Is it permissible for my Father to call me in case of emergency (i.e. Chest pain, Shortness of breath Chass v’shalom)? (2) Is it permissible for me to answer, knowing that the call is of an emergency basis? (3) Can my wife or son answer the phone in my absence (am at Shiur or in Shul)? (4)Then am I permitted to make a call to medical assitance (i.e. Doctor or Hatzolah) from the home of my parents? May they live and be well Ahd Meah V’Esrim Shonim Tovos.
If possible, it is better both halachically and medically for your parents to be able to contact medical assistance immediately without having to go through you as an intermediary. In some places an emergency button can be installed that, when pressed, alerts emergency services. If your parents have problems communicating, then you must be available. Try to arrange a special signal, a special line known only to them, or a Tzomet Shabbat Phone that will minimize shabbat desecration. I join you in wishing them Shnot Briut Min Ha Shamayim.