From Diablo Wiki
Avenger Kills is a feature coming out in the PS4 version of Reaper of Souls. Currently, monsters that kill a player will leave the game and join the game of another player on his/her friends list. However, it will have gained:
- Special abilities
- A purple title (the original player's name).
This process continues. More information has yet to be released. 
No information has been released regarding if it will be included on PC versions.
- http://diablo.incgamers.com/blog/comments/new-ps4-diablo-3-reaper-of-souls-features-revealed/ New PS4 Diablo Reaper of Souls Features Revealed - Incgamers News