Not that you'd end with 16 breeding pens but rather many options to breed. Having two breeding pens is usually enough and you'd be breeding the fathers line and mothers line each spring. You select the breeders by what ever method is important to you. Say you don't care about show quality birds or breed standard of perfection and only want to move your flock forward in faster maturity, size and early egg laying. Well, those are the things you'd keep notes about by tag number or tag color of bird and choose those to breed forward. You have your notes on bird lineage so would choose the most logical rooster with the best traits your looking for. If you want to aid in maintaining endangered breeds then you'd keep track of what's important in the standard of perfection for that breed and color. Close study of the written, and ideal form of that breed illustrations.
All said and done, after so many generations you can select a cockerel from either line and pullets form the opposite line and start all over. Line breeding maintains enough diversity that flocks don't need outsourcing of genetics at all. There are 50 year old closed flocks being bred to standard of perfection. Closed meaning they are not bringing in new blood, they are line breeding. Of course a small backyard flock couldn't maintain diversity that long but larger farm flocks can.
Things that start to happen with closed flocks if there is not enough diversity, needing to bring in a few new breeders, is vitality/vigor of the birds and poorer and poorer hatching rates. Besides undesirable visual traits that may pop up these are important signs of inbreeding and need for a new rooster or quality pullets to infuse into the line.