You have no proof. No pictures. No documents. No artifacts. Nothing.
What if you have a story?
A family member told you something or you overheard a conversation grown-ups were having. Perhaps a particular tale was repeated at informal family gatherings. These passed down stories are often the stuff that shapes our world view. If you're a genealogist or family historian, you grab and hold on to these stories for dear life.
You reach for the name; given or surname. Is it the official name or a nickname? Can the name be compared to others in the family that you are researching? Is this person a friend of the family rather than an actual member? Can anybody alive vouch for this person?
Is there a date in that story? A year or season? Is the story sensational enough to have been recorded in a newspaper? What about location? Where did the story take place?
Once you have dissected the story into its researchable parts, you can go about the business of confirming or denying its validity.
If a story is disproved, it still should remain part of the folklore of the family. It is quite possible that life altering decisions may have been made because of it. Judgments and world views may have been shaped by these stories. It would be up to the genealogist or family historian to put the story in its historical context and frame it as yet still a major part of the family legacy.