The way that asparagus is normally handled is that after the main harvest in the spring, the shoots become spindly and want to grow into the fern. These should be left on to grow through the summer to build the crown back up. If removed, they tend to reduce yields. In the fall, just as the ferny growth has turned brown, it is cut down and removed. Usually this is done before frost. I don't quite follow the last part of your question about the ferns producing end stems that can be pruned. I'm wondering if you are referring to seedlings that occur after the seed drops to the soil below and takes hold. These eventually do produce a plant that is harvestabale, but it takes several years - approximately seven.