It's just like when you have Cats & Dogs pets, or even just household members who didn't come with you-- they're just sort of on hold while you're gone. You won't come home to filthy, starving animals and a chicken coop overflowing with spoiled eggs. When I got to the aspiration goal of foraging 5 times in Bramblewood, well, you have to spend a long time there to make stuff grow, so I rented the vacation house there for a couple nights. The animals were fine when I came home, they hadn't been neglected for a couple days.