Ajax tortures Wade in order to see if he has any mutant genes, which he hopes will bring about his mutant abilities.

Of course, it works and brings Wade's mutant ability to life in the form of being able to regenerate and heal quickly.

His ability to heal and regenerate would explain why his cancer doesn't kill him, though it's still there.

But what about the other people/mutants being experimented on?

For those that also have dormant mutant genes, once the genes are awakened, the reaction would be different for each individual.

For a person who develops mutant abilities that differ from Wade's healing/regenerative ability, would they still suffer with their sickness and eventually die?

Most of the people Ajax is experimenting on are terminal, and they wouldn't have the same ability to keep their sickness in check the way Wade does.