Although the dictionaries suggest translations such as:

رعاية المحتضرين
ملجأ رعاية المحتضرين
ملجأ للعجائز

These Arabic translations are insensitive and cruel to hopelessly sick people. It is adding insult to their suffering. If we back translate the Arabic into English it would sound awkward and cruel such as "Dying People's House" or "Care for the Dying." If we look at the term "Hospice" it doesn't give us that gloomy impression. It is not their fault that they are hopelessly sick. It is humanities fault for failing to find a cure for their illness. If a portion of the money spent on arms and killing machines was allocated for medical research, we would not need to use such a term.

Therefore, I would suggest something more humane and hopeful, such as:
دار الرحمة
دار المنتظرين للقاء ربهم