Those piles of dying plant material at the front of the bed are Toadflax (Linaria maroccana). That is by no means all of them, by the way! I'm leaving their remains in that area to dry out over the next couple of days. When I do remove them, I'll shake them out over the soil to release the seeds that have dried on the plants, thus preseeding that area for next year's blooms.
Conventional wisdom tells us to allow seedheads to dry on the plant before removing them. My experience has been that if I follow the procedure above, I still get a fair number of seeds from the plants, with a good germination rate. However, I do believe it's critical to success that the seedheads or seed pods are already partially dried by the time I pull the plants. Pulling up plants with newly formed heads/pods would probably NOT produce good results. I suspect that if seeds need to reach a certain maturity level before this will work. Knowing when they do is something you have to learn from experience. Experiment with a few plants and see what happens. Poppies are a good example: I've learned that once they begin to rattle in the pod, they can be cut from the plant and bagged to continue drying out.
As for what's going to be planted in that area for summer, I usually have zinnias coming up there. I may plant some summer perennials and fill in with Cosmos. I'm feeling less than optimistic about what summer will bring to my corner of Katy. The high today was 93 and the sun was too intense for me to work past noon. This does not bode well.