People do die of Chicken Pox. Persons who are immunosuppressed or sick in some other way. A normal healthy child, with no other complications won’t die of the disease if, when acquired, is appropriately care for.
However, my point is, if anything, the vaccine may have contributed to the virulence of the strain your daughter had. I’d be curious as to how soon after the vaccination your daughter became symptomatic.
It was two and half years later. She was vaccinated at 6 and developed it at 8.
Although I do question if there aren’t other strains of the Chicken Pox that the vacccine doesn’t cover fully.
Their biggest concern was her eyesight as she got the pox blisters under her eyelids. That was the scariest part for me as a mom and the most horrific thing to see on a child.