If you have to go through a tedious process pickling to make sure there's no botulism, how can you reuse brine?

I’ve heard that if you really like the flavor of some pickles you get at the store, you can just stuff some fresh cucumber slices into the jar and wait a bit and then you’ll have more pickles. If this is true, how is this not risking botulism? You have to do this whole big process the first time around to make sure there’s no botulism, so how come the second time around the risk is gone – or is it? Do you have to keep the brine refrigerated the entire time between the original cucumber slices and the new cucumber slices?