Chemotherapy is poisonous. That’s the whole point of it. (My background is in development/genetics/cancer.)
Different types work in different ways - so one type just hammers anything that’s dividing rapidly which cancerous cells do. Other types zap cancerous cells in different ways, by using the immune system for example.
Cancer is a symptom and a process rather than a monolithic ‘thing.’ A bit like fever - many causes. Many diseases. Many treatments.
A cancer cell has escaped the usual checks and controls that stop our cells from multiplying rapidly and invading tissues they shouldn’t be in.
If she had stage four cancer that means that cells from the primary tumour have invaded elsewhere (metastasis) and this generally is what kills you. If that’s the case then unfortunately the chances of her cancer returning are fairy high. It may take a few years or she may get sick again fast.
Anyway your question: does chemo increase the likelihood of further cancerous developments?
Well it can. Chemo damages and kills cells - that’s how it works. Some methods are more targeted than others. Some methods are so precisely targeted that the chances of knock on effects are tiny. Others are fairly crude but effective. It will depend on what she was offered.
But... if you have stage four cancer and you refuse chemo, you need to accept that’s it. And people do refuse because chemo is hard, and of it’s only going to give you an extra few months and those will be gruelling then that’s your choice and it’s a valid one.
Treatment choices should weigh up risk. So for example if I was fairly young, and had a tumour that was operable (which it sounds like she had) then I’d be very unwise to refuse chemo - the small chance of issues down the line is vastly outweighed by the fact that without the chemo I’m dead, and with it I stand a good chance.
I work in clinical drug development these days and I can assure you that the science side of pharma is not some big conspiracy. (Marketing I reserve the right to consider rather unpleasant...) the process of researching and bringing to market new cancer drugs is done by thousands of very dedicated people who are not in it for any nefarious reasons