I believe I saw this anime for the first time in 2012 or 2013. It could have been as early as 2009 as well. I do not know the name. It is not Soul Eater or Death Note as far as I can recall or determine. The art style is normal anime. It does have some blood but not overly gore from my recollection.
In the beginning, a high school male teenager approximately 18 years old was walking along a street. I believe it was Tokyo urban areas. He was attacked by a large monster. It killed numerous people around him and ate their spirits, presented as a blue flame. As the monster continued to attack, a female warrior appeared, fought the monster and defeated it. The people who were killed did not know they were dead and continued to 'live' for approx 5-8 days, when their flame ran out. I believe they were called lanterns.
The teen, who survived the attack, discovered through the course of the show that he was actually a lantern himself. Somehow he was able to exceed the 5-8 day limitation. He aided the warrior woman in fighting and killing other monsters. Along the way, they found relics, specialized items that can be used to kill monsters. This warrior woman belonged to a limited faction of people who hunted these monsters.
Closer to the end of the show, another woman showed up to assist in the destruction of monsters, because as of late, lanterns appearances have skyrocketed. In the final battle, the teenager and the women faced off with a powerful evil on a wooden roller coaster. At the end, the monster was destroyed and the teen's lantern flame burned out.
