The Short Version
This claim is false. Multiple high-authority CDC and peer-reviewed studies consistently found that unvaccinated individuals died from the Delta variant at 11 to 53 times the rate of vaccinated individuals. Vaccine effectiveness against Delta-related death was 90–91%. The claim likely stems from a well-documented statistical misunderstanding: in highly vaccinated populations, raw death counts among vaccinated people can appear large, but per-capita death rates were dramatically lower for vaccinated individuals.