I assume you are referring to Daylily. It is relatively common. There is a Daylily Forum here but to get you started here is a write up about proliferations

If you have a true lily, and there are tiny bulbs in the leaf axil, then you have a Lilium lancifolium (prev lilium trigrinum) cross, and these bulbs can be planted for propagation. Sometimes when the weather is nice, and growing conditions extend into the fall, these bulbs will actually develop leaves while still on the stem. You can just cut the stem and plant it horizontally/