She can be terminated after her paid sick leave finishes but that termination has to be for failure to complete work duties. You cannot fire someone for having cancer. The letter posted on the CNN article before it was removed said "reason for termination: cervical cancer" which is just ridiculous.
They should have given her a chance and also sat down and had a proper chat. Maybe she'd have said she wants to resign and go home, who knows?
I have a few relatives who got cancer young (30s) and between treatments they went back to work. There were periods they were signed off but it wasn't like they were bedridden for 6 months straight.