The thing to remember with Borrowing with the Witch is the sign of course -
"I ain't dead!". Only the mind is absent - the body is in a state of hibernation so slowed right down which presumably is the purpose behind the sign, as things like breathing and metabolics are slowed right down so it's possible to be interpreted as being dead. Like in other hibernating animals this state can preserve the body for quite a long time - several weeks or even a season and in animals they can survive on stored body fats etc (although apparently bears and higher mammals do 'wake up' occasionally for some essential functions but much less often than usual)
The sign tells anyone who finds the body that the Witch isn't dead and so what does that mean? First off of course they don't get a funeral and once someone knows there's a problem, then another Witch would presumably be sent for and they would feed and look after body until the mind came back - if it didn't then eventually I suppose yes it would start rotting.
We still only have the Esk example of what happens when the mind can't leave the animal host. Granny knew where Esk was so she went back to the eagle's territory and found it in a terrible state, unable to fly and falling about so presumably both the Esk mind and the eagle mind were at odds in some way, which physically affected the eagle's body. This happened after a day with Esk - presumably Granny's mind is far tougher so she can stay longer without getting overrun, but in CJ she and the Count both knew that she couldn't maintain control indefinitely.
As to when Death would come for her - I would hope he came a.s.a.p after the mind had been trapped beyond rescue. It's a horrible thing to think of your mind wandering around without a body to live in.
Also, don't forget that Death cuts the soul away from the dead body - the soul is effectively shackled to the husk/corpse. I think that Borrowing is in part to do with someone having the ability to send their 'awareness' out of their body,
whilst they're still living, so the body is important and this is why Granny 'ain't dead' because her soul/awareness/mind is still linked to her hibernating body...
*
Another aspect of Borrowing - we do have another adept in Miss Treason, the ancient witch in Wintersmith, who's blind and hijacks various creatures, including Tiffany and often uses several creatures at once to use their eyesight and nothing else. For this Miss Treason doesn't 'leave' her body at all as Terry has her carrying on with everday tasks like weaving or giving judgements to the local people. So is that a refined, pared down kind of Borrowing that
doesn't involve so much willpower? Won't go into that so much as we'll be talking about that next week of course
* Gods I think I've been roleplaying far too much recently!