I don't believe phrases or idioms are necessary plagiarism, but it's what you do with it and how you shape the poem that makes it seem purposeful or not. "dig my grave and dig it deep" seems like a common line, as there are not further explanations.
However, anything else added to it to specifically reference the marbles stones and white dove, I would say is plagiarism.
It could be one's subconscious hearing this and applying it to one's poem, and I definitely agree to an extent that nothing is truly unique. Inspiration is one thing, and interpretation, but almost line for line, the same context, is where it gets questionable for me.
Especially since all you have to do is Google the lines, and the origins are from a folk song in the 1920s:
There are many slight variations of the last stanza, but almost all of the poems are the same idea and story. The concept of losing someone to suicide by that method is certainly not unique and has affected people all around the world, but the closing lines and images seem far too similar to ever claim as one's own. Perhaps I'm wrong, and it's unintentional, but I don't really believe in coincidences. Maybe someone heard the original song somewhere, or had the idea passed on to them and, without knowing it, adapted it into their poem, thinking it was their own. Or maybe the imagery of "dig" and "grave" and "marble" and the symbolism of doves was bound to be placed together.