I can tell for sure that exhumation isn't a common practice in Romania. In Transylvania it's, in fact, unknown.
In fact our priests, after the coffin was lowered into the grave, a glass of wine and the ashes of the thurible spred crosswise over the coffin, take the the spade, making the sign of the Cross with it, touching every wall of the grave and saying: "The earth is the Lord's and the fullness thereof; this grave is now closed and sealed in the name of the Father and of the son and of the Holy Ghost, unto the second and glorious coming of our Lord, God and Saviour Jesus Christ. Amen"
If, however, due to some serious reasons, an exhumation has to be done, I assume that a "Panahida" or "Parastas" will be sung.