Grady was a 21st century Human, who was classed as a "dim" and was an occupant in San Francisco's Sanctuary District A in the 2020s. A homeless and mentally-defective individual, he believed that the Earth was being visited by aliens and that he could make himself invisible.
In 2024, he took Jadzia Dax's combadge, but she managed to retrieve it by revealing that she was a good alien, not the brain-sucking aliens that he thought were preparing to invade his planet. She told him that she needed the badge to protect the Earth from its enemies. He gave the badge back and said he would keep her presence a secret. (DS9: "Past Tense, Part II")