the process you are looking for for is called autophagy. It is where your immune system, in the form of phagocytes, search out and consume inefficient/ dying/ damaged cells and harvest their nutrients for reuse in other fresh cells.
Vampire therapy where an aged individual is leached off a youngling, is one way of replacing senescent proteins and cells, but a better way is through intermittent fasting either by way of time restricted eating windows of 8-10 hrs per day, or using something like Longo's fasting mimicking diet (www.prolonfmd.com) which is all the good of fasting without the downside like sarcopenia (muscle loss) which can be irreversible in some elderly, leading to their demise. (Thankfully this can be mitigated with a daily dose of 1-1.5g branched chain amino acids, and the use of exogenous ketone bodies). Heat shock proteins are also a way to induce autophagy, although not as powerful.
The discussion of autophagy raises a key point about a couple of interesting approaches to anti ageing, namely how long would you run rapalogs for given they inhibit autophagy to certain degree, and allow possible free radical production by cells containing damaged mitochondria leaking from disrupted electron chain pathways? The likely answer may be that we cycle this stuff, and have runs of treatments with an underlying persistent effort to detoxify, and unburden our mitochondria, then initiate mitochondrial biogenesis.