This is occurring anyhow. If this person, because of a medical condition, simply cannot go into work for a day, they're not going to work.
If they are out for the week, the same or even greater impact would be on the employer. Is there anything from an administrative perspective that would prevent the system from accommodating a 75-day sick payment versus a 15-week one? Fifteen weeks can be allocated week by week over a period. I don't see why you could not accommodate that.