Answer: The student needs to have a good excuse. If illness is the reason, then you could ask to see a Doctor's note. However you have discretion to judge the validity of the excuse and act appropriately. Other excuses can be difficult to verify or judge. Oversleeping is probably not a good excuse (unless linked to medication), but attending a funeral probably is.
Let us suppose that there is a good excuse. If there is time to accept the work late (for example, if model solutions have not been circulated and answers have not been given in tutorials), then you could just accept the work late and mark it as normal. If it is too late, then you can discount the work, either by substituting an average mark (the average mark for all assignments for that student) or by noting "ill" or "discount" on the marksheet and calculating the average ICA mark over fewer assignments.
Please be particularly careful over projects or tests. You owe it to the conscientious students to be firm with the less conscientious.
If a student has protracted illness and it becomes meaningless to allocate an ICA mark, please consult me and we can work something out.
A tip: you can always keep emails relating to student illness in a separate folder. Then you need only check that folder when compiling exam return marks.
OHK