Being seriously ill is one of the reasons that can be used for self-certification under IRS Revenue Procedure 2016-47 that you would qualify for a waiver of the 60-day rollover deadline, as long as the rollover was completed as soon as practical after the illness no longer prevented you from completing the rollover. 30 days is a safe-harbor provision for this. This self-certification permits a qualified retirement plan to accept the rollover after the 60-day deadline.
IRS Rev. Proc 2016-47: https://www.irs.gov/pub/irs-drop/rp-16-47.pdf
If you do not complete the rollover, having been ill does not prevent you from being subject to tax or to the early-distribution penalty.
