hospice (n.)

1818, "rest house for travelers," especially the houses of refuge and shelter kept by monks in the passes of the Alps, from French hospice "hospital, almshouse" (Old French ospice "hospice, shelter," also "hospitality," 13c.), from Latin hospitium "hospitable reception, entertainment; hospitality, bonds of hospitality, relationship of guest and host;" also "place of entertainment, lodging, inn, guest-house," from hospes (genitive hospitis) "guest; host," also "a stranger, foreigner" (see host (n.1)).

Sense of "home for the aged and terminally ill " is from 1879; hospice movement first attested 1978.