Henrietta Lacks and HeLa cells
The cells never died in the sense that they kept replicating, individual cells still died. They were safely cultured in petri dishes before Henrietta Lacks died. The cells came from a tumor that developed from her cervix. The cervical cancer cells had developed high telomerase activity. Telomerase builds telomeres on the ends of DNA, protecting the chromosomes. In normal cells, telomeres tend to get shorter as the cells divide, eventually the DNA is damaged and the cells die. HeLa cells are protected because their telomeres are well maintained.

There was nothing special about Henrietta lacks that made her tissues immortal, so digging her up wouldn't be worth it. Her family would probably get mad too.