What happens if someone with blood cancer donates blood?

Probably nothing: Most people with leukemia are likely to be anemic and not pass the screening. In the unlikely event that they are unaware of their illness (for example, mild early cll), the donor's body is almost certain to reject the foreign cells as from an unmatched transplant. I've never heard of leukemia transmitted by transfusion. And we screen for htlv-i.