Board Thread:Lore Discussion/@comment-86.24.50.100-20130623082136/@comment-1600847-20140825180737

There are descendants of the Septim bloodline still alive as of the 4th Era, the Kings of Shornhelm. Andorak Septim, son of Uriel Septim IV,  was removed as Emperor by a majority vote by the Elder Council, but they weren't utter dicks so they made him King of Shornhelm in High Rock, where his descendants still rule. So technically, there are still direct members of the Septim bloodline still alive. I think Bethesda just forgot about them, though :P

http://elderscrolls.wikia.com/wiki/Andorak_Septim