Rachel, one way to pull nails after the head breaks off is with a nail puller. It's kind of hard to describe, but it has jaw that grip the shank harder the harder you pull. Usually the way it is used is by setting the jaws on either side of a flush set nail head then useing integral slide hammer to drive the jaws into the wood and under the head. You can use them to pull a headless nail, but if the nail is rusty and/or the wood very hard, they may just bite a piece of the nail off. They cost about $40, so be sure you can return it if it doesn't work for you. Another option might be to just drive the headless nails in then set them deeply with a nail set.