Does Power of Attorney rights void after the person passes away?

If you have POA over someone and have control over all of their financial
affairs, what happens to their money thats left in the bank if they pass away?

A power of attorney dies along with the person who granted it. Whatever they had when they died should be dealt with by their personal representative.

Yes it does only if there is an expiration date of the power attorney application. You may want to consult with a lawyer to verify this information. These applications are only good for specific purposes only. It doesn't mean that the POA gives and individual full rights to make descisions. It depends on what your using the document for.