quote from
"Cell Death: Apoptosis versus Necrosis"
Department of Microbiology and Immunology. New York Medical College. (http://wwwuser.gwdg.de/~smirono/WahlFach/Apoptosis&Necrosis.pdf)
"Preliminarily, we suggest that to compare apoptosis to necrosis is scientifically unjustified. It is unsound to compare the process whereby cells die, i.e. cell death, and the changes that the cells and tissues undergo after the cells die, that is necrosis. These two processes are temporally dislocated and represent the two extremes of a continuum: the necrosis process can start only and exclusively when the cell dies and is an irreversible process, a 'no return' way in the cell life (Popper H., "Hepatocellular degeneration and death" In: "The Liver. Biology and Pathobiology" Raven Press 1988 pp 1087-1103)."

So your worry about apoptosis and necrosis was based on previous misconceptions. Whether naturally or unnaturally, cell death is cell death, and the body has to clean up the remaining debris. But I don't think any of the alternative ways to kill tumors kills them all at once. So your liver and kidneys aren't overburdened. For instance, to acidify and kill a tumor using electric current (www.altcancer.com/emf/eng/DC.html) takes 3 weeks which spreads out the destruction enough not to overburden your system.

Even if the previous view of cell death was correct, how could you induce "programmed cell death" (apoptosis) in cancer tumors? I don't think you can. You have to induce traumatic death to cancer cells/tumors. That's what your immune cells are trying to do to the cancer cells.