Yes. Egg production slows down in most chickens, around age 3-4, some continue laying for life, but health problems are not uncommon and will usually arise between the same ages the production will slow down. Chickens can live up to 5-7 years.
Chickens are no different than us as we age. Things stop working so well. Some "breeds" specifically raised for egg laying like the Golden Comet (a cross breed) are only good for about two productive years before laying falls off prodigiously, and the bird itself is often not much far behind. Other breeds, slower to grow and start dropping eggs, who produce eggs less frequently will tend to produce eggs over a longer period, and their decline in production won't be as noticeable. (i.e. when a Comet goes from 6/wk to 3/wk, its obvious. When another breed goes from 3/wk to 2/wk as part of a small flock, that might skip your attention for a time - even though they've both dropped 50%)
Most hens will produce fewer eggs as they grow older, and there will be big differences between individuals in the flock. Given good care, diet, etc, genetics and luck matter. Predation may remove some hens, so they aren't going to reach their full lifespan. Then nearly nobody breeds for longevity, so when parents are all under two years of age (or maybe one year old) there's no way to know who might do better longer. It's about the economics of egg production, and both production and fertility will drop off over time. ESPECIALLY when it's ignored in breeding stock selection.
Heritage breeds might do better longer, but again it's about parent selection.
If you plan to breed birds in your flock, your choices will make a difference in future generations.
Many chickens will die by three or four years of age, although there are some who will live much longer. My oldest hens have been ten years of age, and weren't laying eggs for some time before becoming ill.
My youngest pullets dying of reproductive problems were one at six months, and recently, one at seven months of age. Miserable!
Some very few chickens will live into their teenage years. A Cubalaya breeder told me, years ago, that it's more common in that breed.
Each chicken is an individual, you an never tell what one specific chicken will do. Most hens molt once a year and stop laying while they replace their feathers but occasionally you'll get one that lays an egg even when molting. You can't use words like never or always.
Some hens stop laying when they get a bit older. Some continue laying even when they get pretty old. Most lay pretty well for a couple of laying cycles (a laying cycle is between molts) but then drop off production after each succeeding molt, often dramatically. If you have a large flock you may be able to say what the flock will average over time but that does not apply to one specific individual.