I believe Mark Twain once wrote a letter that would be very appropriate for a situation like this.
It seems to be the case that when low on nutrients but healthy, the body enters a certain state of preservation. This could slow down the formation of blood vessels to cancerous tissue but i doubt it will prevent it.
Starving the tumour doesn't work, because it will pull whatever it needs from the blood and surrounding tissue...kind of like babies. It's the rest of the body that will suffer.
Also, trying to halt angiogenesis with diet won't work particularly well, because the idea of a cancer is that a lot of it is ischaemic and necrotic anyway. Angiogenesis inhibitors work, but what is required is far beyond the little (if anything) that is achievable through diet.
On a side note, it is even mentioned that consuming a low amount of calories can prevent a woman from getting pregnant. Although not relevant it is certainly interesting. I personally would not bet on it. Evolution makes people a bit different. And this is great for survival. What works for one person may not work for another.
Weight gain/loss, extremes of body weight, exercise level, diet, a lot of things can make a woman anovulatory (and therefore temporarily infertile).
To return to the subject, it is his mothers choice and hers alone. But it depends on the situation , by giving this real life example : Recently the stepmother of a very nice person was diagnosed with cancer. The chances of survival even with chemotherapy and radiation therapy and surgery were extremely slim given the age and the progress of the tumor. The stepmother opted for the decision to be with family for the weeks she had until she would pass on. I can not give all information of course because of privacy reasons. Needless to sat that this is an understandable situation.
But refusing a sure chance of survival and going for homeopathy. I find that difficult. I myself constantly try to point out in my virus thread that the cause of cancer and other diseases is not as clear and easy as some doctors point it out to be. But there is hope for the future as we make technological progress.
Well, it's not just the mother's decision, because she doesn't have to live with her death. Her family does.
Also, I agree that given that not all the information is available in this case it's hard to make a concrete recommendation (nor should the OP take it without consulting an oncologist or general practitioner first). But homeopathy is at the very, very bottom of the ladder for what may improve your outcome in terms of cancer treatment. While a lot of chemotherapeutic regimens are designed to be curative, there are a lot of treatments designed to be palliative. Even if the illness is terminal, treatment can be designed to slow progression, especially into important areas like nerves or vital organs, increase lifespan, and improve quality of life. Whereas the only thing that homeopathy could possibly do is to decrease pain very, very slightly due to placebo responses.