I've grown Asphodelus acaulis for many years and in that time have had 2 seeds one year and 1 seed a few years later. None germinated though I'm sure they were good. The seeds were large, black and lumpy, like a Zephranthes or Hosta seed but much thicker and 3 dimensional, and not glossy. Maybe about the size of a piece of chopped walnut such as you might like sprinkled on top of a cake or about half the size of my small finger nail (I have smallish hands). The pods were rather like those of, say, Anthericum or Albuca but with very short, curled stems. The later seed is still in its pot but is 4 years old now and nothing happened. The plant itself didn't flower this last winter as it had been overgrown by grass and I had to rescue it. So no seed coming along. In the future I'll try hand pollinating and see if that gives better seed set.
Even though the plant is winter flowering, I don't see why that should make it less likely to set or ripen seed, since that's it's natural way, the RIGHT time for it to do those things. It may be more likely to seed under glass. Mine is in the open garden at all times.
