Is there any way to counteract the calcium chloride included in most canned beans? All the beans I can find in the local supermarkets have calcium chloride in them, which helps them retain their firmness.

But I want soft beans. 

Yes, I can cook my own beans from dry, but sometimes I just want fast access to beans. Beans that will be soft and break down in soups or stews.

But beans treated with calcium chloride just sit there, even tasting a bit undercooked in the center. Is there some way to counteract the calcium chloride so that they will break down and get soft?
Calcium in Calcium Chloride indeed firms the beans by fortifying the pectin.
On the other hand, alkali conditions will greatly accelerate the breakdown of pectin during cooking. 

You can simply use baking soda to soften the beans while cooking.