I usually leave the plants to turn brown , then when I take them down there will always be enough beans for next year's planting, but I have noticed where the missus dropped some that were too developed and stringy they have turned purple as the pods turned brown. The most important thing I find with runners is to dig out a trench and fill it with organic matter that will hold water, they are not so needy of actual compost, they make their own nitrogen. People say they put nitrogen into the soil, but of course they don't, they make it for their own use, but if you chop off the halum for the compost and leave the roots to rot in the soil you will get the benefit.
They are one of the best looking vegetable plants, I also grow a variety called St. George which has red and white flowers, the seeds are almost white and easily distinguished from the scarlet runners. Climbing french beans have pretty violet flowers, freeze beautifully, and have a longer season, worth considering. There are advantages to saving seed beyond the economic ones, they select for the growing conditions in your garden. Someone did a study of immigrants who had brought exotic vegetable seed with them and grown them in British allotments, they found that after ten years or so they were doing far better than varieties specially produced for the British climate by seed companies.