Wellllll, we have kids to help out. We had the flu really, really badly right after Christmas, and we were ALL sick. So, we just did the bare minimum for about 2 wks, and had to make up for it when we were well again. I remember being out in the rabbitry cleaning poo and raking and ended up only doing the hutches w/the most rabbits because I got to the point where I was honestly afraid to be out there by myself. The kids were all in the house helping to watch the 3 yo and I almost passed out. I felt that coming and decided the rest of the rabbits would just have to sit on a bit of poo 'til I could get out there again. They lived. We would keep spare water bottles (our semi-automatic watering system kept freezing up) in the house and whomever felt like going out would take a bag of bottles to replace and toss them some food.
The chickens got tossed some feed a couple of times a day, and we managed to get them some water. The goats got hayed and watered (thankfully we have a heated water bucket) and fed and we just got by somehow. You just find ways to make it.
If I'd had to deal w/a garden, I don't know what would have happened, but I'm sure we'd have had some big ole veggies, and maybe some overly ripened, but again, we would have figured it out.
One thing we really try to do is just be prepared. Have plenty of food in the house, plenty of wood chopped, plenty of drinking water. Keep feed and hay stocked up at all times.
Mind you, we do not live off-grid, but we do homestead.
Oh, and we do have neighbors I can call on for help if we really need it.