Dietes grandiflora (Wild Iris).

Rose

I agree with Ken that it's a hyacinth that's been there for a number of years. IME they bloom really fully the first year, but after that the size of the bloom cluster is smaller. To my eyes it looks fairly similar to the one that has been in my garden for a number of years (but I like the color of yours better than my pink one.) "maybe I'll be moving it in the house later on." It is natural for bulb foliage to die off a few weeks after the spring bloom - they do it here in NH. I would leave it outside. Many bulbs need the chill that being outdoors provides, though I don't know if your winter is cold enough to provide very much chill. (nighttime frosts in winter?) If it's near perennials that will cover the area after bloom you won't even notice that it's disappeared.

It looks more like a fall blooming perennial aster, Symphyotrichum novae - angliae to me. When was this picture taken? Is the plant in the picture above blooming now? It really has all of the characteristics of a Dwarf Fall Aster but they don't start blooming until late August or September. It looks like good ol' Aster 'Purple Dome.'