Players have discovered that surviving a Tier 11 delve without dying unlocks a title on live servers!
When you complete a Tier 11 delve without dying, your character will be awarded the 
Immortal Spelunker achievement and the Immortal Spelunker title.
Recently, two players have confirmed that they received this title on live servers.
Other Delve Titles
In addition to the Immortal Spelunker, there are other titles available through delve content. For example, completing a Tier 8 delve without any deaths will earn you the 
Undying Caver title, matching the corresponding achievement.
Finally, there’s the High Explorer title from the 
That Extra Push Over the Cliff achievement!