A hospice was a medical facility for end of life care.
Mai Duyen Trinh considered hospice care following a debilitating accident, but chose instead to be cared for by her mother Nguyen Thi Yeh during the last year of her life. (TOS novel: Allegiance in Exile)
Suffering from an incurable blood disease, Diego Reyes's maternal grandmother spent her final months in hospice care. (VAN novel: What Judgments Come)
In 2381, when Seven of Nine was no longer able to provide constant care for her aunt Irene Hansen, who suffered from Irumodic Syndrome, she was placed in hospice. (VOY novel: Unworthy)
Elias Vaughn was transferred to a hospice at the Vanadwan Monastery on Bajor after the Borg Invasion of 2381. He died there in 2383. (DS9 novel: Raise the Dawn),
Radovan Lena died in a Bajoran hospice in 2379. (DS9 novel: Original Sin)