Rebirth

In the Underworld, you can be reborn by getting dipped in the River Lethe to erase your memories and being born again in the mortal world.

The Heroes of Olympus
Since The Doors of Death was opened during this series, some souls slipped out of the Underworld causing the person who died to be reborn, still with their memories.

The Son of Neptune
In The Son of Neptune, during a game at Camp Jupiter similar to Capture the Flag, Gwendolyn died but her soul escaped through the Doors and came back to her body.

On The Quest for Thanatos, Frank Zhang and Hazel Levesque shared a blackout. Hazel went to the Underworld with Frank, explaining to him about what happened after she died. In The Fields of Asphodel, Nico di Angelo came to try to find his sister Bianca so that he could bring her soul out of the Underworld, but brought Hazel instead. He explained to Hazel that Bianca had been reborn, and he would never see her again.