Mine reseed themselves like crazy. In late fall, I take the dried plant from the pot, and just sprinkle the seed heads wherever I might want some in my garden beds, or in the pot.

Never for me. But the only things I can get to come back from seeds are weeds!

I have some in a large shallow pot out front. I pull the dead plants after a freeze and now I have tons of tiny seedlings in it. They are slow and take awhile to grow back. They need heat to thrive. I seeded that pot once a few years ago and haven't had to add any new plants to it. I just have to remember to water it once those little things sprout. Its easy to forget since you don't see them unless you look closely.

Each plant will die when it gets cold, but it will leave lots of little seeds if the flowers were pollinated. If the seeds can take where they fall, then you will get a constantly regrowing moss rose area, year after year. Otherwise, you'll have to manually collect and put seeds where you want them.

Purslane acts this way also, in case you want a pink-flowering purslane plant.

Pink rain lilies are also cute. They will naturalize by making more bulbs, but you can also plant seeds, which mature very fast from the seed pod. Otherwise, they are perennial.