Final answer:
The doctrine that allows states to declare federal laws null is known as nullification, which was supported by the Virginia and Kentucky Resolutions but curtailed by federal legal supremacy.
Step-by-step explanation:
The theory that allows states to declare federal laws null or not valid within their borders is known as the doctrine of nullification. This doctrine was articulated during the early years of the United States, most notably in the Virginia and Kentucky Resolutions, which stated states had the right to nullify federal laws that they believed exceeded the powers granted to the federal government by the Constitution. However, the legal and political debates, culminating in decisions like the Supreme Court ruling against Maryland's attempt to tax the National Bank, established the supremacy of federal law and curtailed the nullification argument.