In Attack on Titan, the titans wandering around the walls seem to live longer than 13 years, bypassing the curse. We know for sure that the normal titans live longer because of the Smiling Titan.
But why aren't the wandering titans affected by the curse? Shouldn't all the titans have died just because of this curse?
The following answer contains spoilers from chapter 88 and after. (For those who don't read the manga: it's WAY beyond the anime)
As we know from chapter 88
among the "subjects of Ymir" there are always up to 9 people who inherit the power of the titans, a piece of Ymir's "soul" or power, which allows them to transform into one of the nine "special" titans. Along with this power they inherit the curse of Ymir, which is the reason they die 13 years after awakening to their powers.
On the other hand the "normal" titans were originally
"subjects of Ymir" who were transformed into titans by injecting titan spinal fluid into them. But they did not inherit the original titan power, so they didn't inherit the curse either.
Regarding the special titans,
the 12 disciples of Ymir die in 13 years, so only the Shifters die in 13 years.
But normal titans
were turned by force, so they would not have died 13 years because they did not inherit the titan shift unless they eat a titan shifter, which will start the 13-years timer.
However, for Eren's case,
his 13-years timer started when he first turned into a titan.
So the conclusion is,
when you eat the titan shifter, you have to wait until you turn into a titan to start the 13 years.
