I am assuming that this person was given all of his accrued/unused paid time off work prior to leaving your workforce, as that would have been the right thing to do.
I am also assuming that you either offered no disability insurance coverage through your company or that this employee did not opt for that coverage. If he had that, he would qualify to be paid at least some portion of his normal compensation while he is disabled due to serious illness for whatever period of time the disability policy allowed.
If you employ 50 or more people, you may want to refer to the FMLA regulations, as if the employee worked the requisite 1,250 hours in the preceding 12-month period, he is entitled to 12 weeks of unpaid leave and his job back. In this instance, he could not collect unemployment as he is off work due to being disabled.
If you do not employ 50 or more employees, the answer would be that in order to legally collect unemployment benefits, the person is supposed to be capable of seeking employment and commencing a job if/when one is offered. An individual in cancer treatment would not qualify.
He may be eligible for some kind of social security or other assistance (such as food stamps) while he is unable to work.