According to Dog Star Daily, the idea that dogs run away to die is largely a myth. Most dogs that do not come home are lost, hurt, stolen, picked up by strangers or taken to an animal shelter.
Most dogs wander off occasionally, given the chance. Dogs are basically domesticated wolves, and the impulse to roam, hunt and explore is inborn; however, they tend to return home under their own power. Dogs are generally well-equipped for finding their way, but an old dog is more likely to become confused and get lost. Considering the close bonds dogs form with their human families, it is reasonable to assume they would rather die in the comfort of home.