They buried her in the family tomb (1)
So, there's nothing specifically supernatural in this line, but we can't help but think of ghosts and life after death, when we think about tombs and cemeteries. This poem isn't really a scary ghost poem, but it definitely refers to the eerie side of the dead.
and in the depths the dust of what was once her husband trembled: (2-4)
Now we get down to it. First of all, we have the idea that the husband is actually dust. This would take a long time, probably more than the woman's life span, to happen. Second of all, it's considerably unlikely that his dust is actually trembling. If he's in a coffin, we doubt any wind from the outside would reach him. Yet, the point of this poem is not to be scientifically realistic. Instead, it pushes the boundaries of the possible so that we can get to emotional reality—the way that the speaker imagines this husband receiving his wife, after so many years alone in the tomb.