That is highly doubtful. Cancer will surely not evolve to fight the successful cure. Each cancer has to start its micro-evolution from 0, since they can not survive to pass its progeny to other hosts. Each cancer has its own space to evolve and different spaces do not communicate. If there is a cure, you are basically reverting its evolution to day 0. All cancers use similar mechanisms because of concept known as convergent evolution.
Once cure exists - the real cure, meaning no single cell is left from original cancer that survived the latest 'cure' to then pass its genes to its progeny (which is maybe impossible, who can say) - there is no risk to adaptation to the cure.
Now, I can imagine scenarios when this would not hold - for instance vertical genetic transfer to different hosts via some infectious vector but that is probably highly improbable.
> All cancers use similar mechanisms because of concept known as convergent evolution.
First of all, this hypothesis is still highly contested in the literature. There are no doubt certain pathways (usually part of cell cycle regulation) that happen to be used by most cancers, but there are hundreds of genes involved in the cell cycle and we aren't even close to enumerating all the ways that it can malfunction. The fact that most cancers use similar pathways is no doubt reflective of the fact that they are the easiest pathways toward malignancy, not the only pathways.
Secondly, say we do take the top N common mechanisms and create a bulletproof inhibitor. Now your statement about convergent evolution is no longer true. Anything that kills cancer cells (excision, radiation, chemotherapy, something targeted) exerts selective pressure, and you will instead start seeing cancers that utilize the (N+1)th easiest pathway, (N+2)th, and so on. It's like trying to stop all the ways that a car could break down: possible up to a certain point, impossible in the long run.
I also contest the statement that "you are basically reverting its evolution to day 0". Germline predispositions for cancer are an important part of the disease and not selected against in a society where people have natural-born kids between 20 and 40. If there were a cure for cancer, it would probably involve genetically engineering humans that are extremely unlikely to get it (and also age very slowly, etc.). But then you are looking at a totally different kind of society.
> genetic transfer to different hosts via some infectious vector but that is probably highly improbable
This is not only probable, it is known (so far, 12% of human cancers). Viruses linked directly to cancer include HPV, EBV, HTLV, and polyomavirus [1]. A virus that causes cancer can be a very successful virus, depending on how long the infectious/replicative phase is compared to the symptomatic phase. Replicating infected host cells = more viral production = greater likelihood of survival and transmission.
There are some researchers that think that all cancer is caused by viruses that have yet to be identified. I don't think that's literally true, but we can find all kinds of remnants of ancient viruses in our genome, so in a way, they might be on to something.
Once cure exists - the real cure, meaning no single cell is left from original cancer that survived the latest 'cure' to then pass its genes to its progeny (which is maybe impossible, who can say) - there is no risk to adaptation to the cure.
Now, I can imagine scenarios when this would not hold - for instance vertical genetic transfer to different hosts via some infectious vector but that is probably highly improbable.