The cow will stop producing milk eventually unless they get a bull as well. Milk is produced only for a time after calving. Although of course they can always take the cow back to the farm for breeding. The farmer likely would ask for a little bit of compensation, but it would still be cheaper than having their own bull just for the sake of one cow. That being said, they obviously can't milk the cow around the year, so with only a single beast, there will be a period without milk.