The research suggests that a lot of the toxicity of chemotherapy to the patient (as opposed to toxicity to the cancer) doesn't actually come from the chemotherapy agents, but from the body's reaction to it. Specifically, some cells in the body, like white blood cells, get ravaged by chemotherapy drugs. If you suddenly kill off a lot of white blood cells, the release of natural compounds within the cells leads to a lot of the acute symptoms like nausea, weakness, etc.
A 72 hour fast, however, forces your body into a protein-recycling mode (autophagy, consuming one's self.) It turns out that a 72 hour fast causes the body to re-absorb, on a controlled basis, about 1/3 of the white blood cells - and the cells that are re-absorbed are the weakest/oldest/most vulnerable. The same cells which would be most likely to die immediately if you take a chemotherapy treatment. The healthier/stronger cells survive the fast, and survive the chemotherapy.
So fasting before chemo is a potential way to reduce the shock to your system... and afterwards, when you start eating again (refeeding), the body replaces those lost blood cells... with healthy new ones!
In theory, the same effect can be at play in other bodily cells, but the best research, so far, has been on white blood cells, which are easy to sample and count and analyze. I've had no chemotherapy, but I like to play with things, and periodically replacing my oldest/weakest cells with healthy young ones sounds cool.