Not rapamycin, but interesting wrt not dying of cancer. I would guess that proactively exercising (that is, when one is healthy) might help cause one to not get cancer in the first place.
https://www.the-scientist.com/news-opinion/how-exercise-helps-mice-fight-pancreatic-cancer-70134
the researchers found that aerobic exercise activated interleukin-15 (IL-15), a cytokine typically released by muscles during exercise, which triggers inflammation to fight pathogens. That activation mobilized a subset of CD8 T cells—immune cells that target and kill cancer cells—that carried an IL-15 receptor, ultimately allowing them to better infiltrate and engage with the tumor. The mice that exercised were found to have more of these CD8 T cells in and around their tumors.