Yes, you can, with green beans and dry beans. It's like making sauerkraut, but with beans. Look for a good facto-fermenting recipe.

I don't mean facto-fermenting. I mean literally leaving them out to soak on the counter.

Wouldn’t they start to spout?

If you soak them in a brine, that’s saltwater- they ferment. If you keep them fresh and rinsed, they will sprout. if you let them just soak in regular water without changing it, they will rot.