Let your beans go
By now climbing beans should be past their best and pods will be turning stringy and getting tough. Don't give up on them though, leave plants so that they can ripen as many pods as possible.
When the pods are beginning to dry out they can be harvested and the beans inside can be stored. You can use them through winter as you would a kidney bean or dried cannelloni bean - they also look beautiful and make good counters for card games!
Leave the fleshy roots in the ground and - unless you get hard frosts - they should re-grow just fine next spring when the soil warms up again.
Get growing without soil
If you are renting, live in an apartment, have no access to a garden or live in a part of the country where winter weather can be cold and harsh then think about filling a bunch of containers with potting mix so you can still enjoy a reasonable harvest through autumn and winter.