The starter is a living thing. It is made of a combination of yeasts and bacteria. When you feed these with flour and water they will multiply and grow. The way you typically make sourdough bread is that you use some of the starter in the dough but replace the yeast and bacteria you used with flour and water. The starter will then grow back to its original size. You can do this essentially forever.
Old starters is kind of a novelty though and might not mean that much. There are a lot of bacteria and yeast in the flour you feed it with which comes from the fields where the grains were growing. So the original yeast and bacteria from 100 years ago could easily have died out and been replaced without anyone noticing.
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