Will a chained Dog starve?
Solution 1:
Animals which don't require a pasture can be safely chained (or better yet against ambushers: put in a sealed raised glass box outside the entrance) for as long as you want to, though they will obviously die of old age at some point and need to be replaced. This includes dogs, cats and pigs from the default "domestic animals" list.
See also: How do I stop animals from starving?