The old flower stems die, and go brittle by which time a lot of seed may have been amassed in the heads and still be there unless the wind has knocked the stems about and it's been scattered. If you want that just scatter it about, yourself, or collect it (it probably won't come true, but it's fun to see what does come up), and cut off the flower stems. I have to say, I never bother, but break them off and lose them in nearby vegetation!

I'm careful to remove the dead flower stalks before they seed everywhere or they can take over the garden!