The point of the deadline is not that you can't be off work, but that you stop getting paid for not working.

For example, the way it works in Australia is that after you have used up your sick days, you have to take any further absences from work out of your annual leave balance, and once that is exhausted, you switch to leave without pay.

I had a downline team member who once needed to extend their time away from work for over 5 months due to illness. They had been with the company for several years at that point, so they had a reasonable sick leave balance, probably 10 weeks. When it became clear that they needed longer, they used their remaining 4 weeks of annual leave, then took a month of leave without pay, then another. They were still employed, I approved their leave requests each time they needed to extend, and we just used the most appropriate tool that was available at the time.

The thing you're getting permission for is not to be sick, it is to be considered still employed while not doing work, rather than being fired/disciplined for being AWOL.