The cloak has been handed down since Ignotus Peverell. The ring or stone had the symbol for the Deathly Hallows on it, which was mistakenly called the Peverell coat of arms by Marvolo Gaunt. That ring had been in the Slytherin family for generations. Probably distant cousins. Or the ring could have been stolen. Yet claiming to the ministry worker that he carried the Peverell coat of arms seemed to indicate that the name was important and indicated that he was a pureblood and of Slytherin's descent.

Interesting.

She has left this open to interpretation. I'm assuming they are related somewhere back there.

What is interesting is that dumbledore could not wear the ring, yet Marvolo Gaunt did. Also Umbridge was not affected by the locket, yet Harry, Ron, and Hermione were.

Just some thoughts.