The best way to tell or know if cooked beans have gone bad is to smell the beans.
When the cooked beans have actually gone bad the cooked beans will have a very sour smell to them.
I had unplugged my slow cooker before after cooking the beans and having some leftover beans, then as I was letting it cool down I had to go visit my Grandma in the hospital and then had to stay a few nights in a hotel because the hospital was away from home.
I came back 2 days later and the beans in the slow cooker smelled really sour.
I had to dump the beans in the trash and then wash the slow cooker out.
When the cooked beans go bad even when refrigerated they will take on a sour smell or also sometimes have mold growth in them.
If the cooked beans smell or have mold growth or you've left the cooked beans out overnight then they should be thrown out.
Uncooked beans can last for years before they go bad.
If the uncooked beans have any mold or other discoloration on the uncooked beans then they should be thrown out because they have gone bad.