On the last page of the manga we see a shadow sitting on the old desk carving the words "who is the dead person," what is your interpretation on this? For me, I believe the engraved words are what initiates the curse. And since everything related to the incident is erased from the world once the curse broke or has completed its course someone needs to revive it. But the question is who? Discuss your theories here.

26 years ago when Teachers and students acted as if there beloved student hasn't died, it was out of love for her. But in the graduation photo she appeared which means she couldn't 'spirited away' because of feelings of her fellow students and teachers. Maybe it made her spirit angry that she started taking life of someone every year, and that someone becomes 'another' for that year. Or maybe previous 'another' take life of the person who becomes next year's 'another'. Or maybe there is no exact force that make 'another' (since it doesn't occur every year). It isn't very clear why the curse started in the first place, and how it is carried out every year. Probably person who is 'another' for that year kills off the students.

that desk is probably not as old as the old furniture are left in the old classroom. it's not the word but rather the students behaviour of pretending that a dead person as living is the one that initiate the curse. probobly the year after someone died in the class accidently but nobody did the same for him and he become sore. somehow the anger become too great that it become a curse, and then a chain curse on the coming years

So...

what exactly happened at the end? Did reiko's death break the curse completely or did it fulfill the year's offering?

Most probably it will continue next year, since fifteen years ago when a student killed the 'another', the curse continued next year.