How do heirs pursue an estate when no will was left?

When somebody dies without a will, inheritance from that person is determined by state laws of intestacy. Your father's cousin had heirs at law, and they are determined by the law of the state where the cousin lived, so you may be someone who would be inheriting from the cousin. The heir finder may have found the cousin's name at a website such as missingmoney.com, then researched the cousin's family tree. You may want to check that website and the state treasurer's offices in all states where the cousin lived to see if there are unclaimed funds listed there. They all would probably provide you with guidance on what the process would be to collect the funds.