The blooming rosette will frequently die before the flower stalk and seeds fully mature. I sometimes will pull the dead rosette from the soil and put the seed stalk in a paper bag to collect the seeds as the capsules dry and mature, rosette and all. The seed stalks frequent die/dry out from the bottom up as the seed stalk is consumed by the developing seed capsules, so you have the option of cutting the stalk away while the seeds are still maturing.
