The main bulb may have gotten destroyed, weather, moles etc, but not killed, leaving the bulb scales in the soil, these will root and grow with ease.
You may even have planted a bulb that had a rotted root plate and it cause the same effect, one large plant becomes many small plants.
Depending on the type of lily, it might have even been leaf bulbils falling and rooting up.
All just guesses but that my first thought, rooted bulb scales.
