[mybooboo]

Not really understanding your first example. As "influence" is the memory others have of you and really isn't a rebirth so to speak. And our base elements do exist after the decay of the body it was part of.

I follow the Mahayana school, Gelug to be specific, and the Mind is what carries on to the next existence, in which your Karma decides what that existence would be. Creating positive Karma should help to allow another precious human birth in which you can further study the Dharma and progress on your Path. Or possibly a Pure Land, depending on your Karma from previous existences. But also negative Karma can cause a birth in a lower realm. Such as the animal or Hungry Ghost, Pretta, realm. In my understanding the cessation of Samsara comes after one has the positive Karma to become a Stream Enterer, and is nearing Enlightenment. Which would also be the cessation of dukha or suffering.