There are some narrations indicating that the believer (mu'min) and/or those who have allegiance (wilayah) to Ahl al-Bayt (A) are created from a specific sort of clay, which is sometimes associated with the Euphrates. The faithless (kafir) and/or enemies of Ahl al-Bayt (A) are created from another sort of clay. And most people are of a sort of mix between the two which is why we have diverse temperaments.
Anyway, if these narrations are correctly transmitted, they seem to be more metaphorical about our natures and not literally relating to what kind of components we are physically constructed from. In fact, given that we human beings primarily gain our physical material from eating, and food is imported and shipped worldwide today, we are often built from the "clay" of many different regions!
So with that in mind, it is reasonable to say that someone with a strong affinity for Ahl al-Bayt (A) might have some creational link to Karbala metaphorically or metaphysically.
That being said, I am not aware of any text that indicates that we are buried in the same place whose clay we are created from, or which really assigns any significance to the region where we are physically buried.
In fact that Qur'an tells us that we don't know what land we will be buried in; life is full of surprises and we never know where we will go, nor when we will go.
Similarly the Qur'an does not assign any particular ethical significance to where we live and just says that Allah's earth is vast and if we are unable to live freely in one area, we should move.