Sorry to disappoint, but he did NOT finish the LN
He died on April 4th this year, volume 20 of the LN was published on February 25th 2011 in japan
He planned on making 22 volumes, leaving 2 volumes missing
He had to stop with volume 20 because his cancer got worse and he didn't get to make the 2 final volumes anymore
We DO have an anime adaption though, 4 seasons with 12-13 episodes each
The first three seasons were made a few years before he stopped working on the LN and then, a year after his death a fourth (and final) season was aired.
As the author wasn't around anymore, they had to create their own ending though and they sure did a good job with that
RIP Noboru Yamaguchi
Looking for translated light novels?
Baka - Tsuki
There are MANY translated light novels, including Highschool DxD, Toaru Majutsu no index, Infinite Stratos, Seirei tsukai no kenbu AND Date a live (the Manga adaption of which got cancelled after chapter 6)