Chickens can still lay eggs for more than 3 years. We have a couple of Silky bantam hens that still produce a couple of eggs a week and they are about 7 years old. It's just not commercially viable to keep them long, but for a hobbyist they can live up to ten years.
As for feeding them, chickens will eat anything, ours get all our leftover fruit and vegetable scraps. "Chicken feed" is synonymous with cheap.
Chicken poop is ideal fertilizer as well, it can be blended into soil without composting.
And, if you like thinking about SHTF scenarios, having some chickens around is a good idea.
OK ... my bad ... what I should have said is I'm not feeding a chicken unless it is producing regularly ... and a couple of eggs a week is not productive IMHO ... any chicken that get the honor of living here needs to be prepared to meet it's maker right around it's third birthday. Unfortunately at my house we don't generate enough table scraps nor have enough land to make feeding them cheap.
And SHTF or not, I MUCH prefer the taste of fresh home-raised meat and eggs over store bought.
Are you sure about the not composting the chicken poo?? We did that with rabbit droppings but I was always told chicken poo was too hot (like horse and cow manure) to use fresh so it always went into the compost pile.