It probably depends on the wording of the personal guarantee, but assuming the guarantee is in event of non-payment by B, you can go after A.
Now you still have a duty to mitigate damages. What that means is basically you can't just leave the place empty. You have to try to get someone else to rent it. Now you have to charge the new person (call him C) a reasonable rent. You can't charge him a dollar. But, if you can't get the same amount now because of the drop in the economy for instance, you rent it for what you can get, then you can bring an action against A for the difference.

