By the time my wife died, I had been deeply involved in caring for her for a long time. The moment when she died brought me into a new phase of grief, which of course started before the very end.
You then have the additional burden, as you say, of planning the funeral and winding up the estate. By the way, if you wanted time for that, you'd probably have to give somebody a year off. The important thing to say is that caregivers do have this additional state of exhaustion and building grief that is on top of what may afflict other people who are close to the person who's passed.