This is from Inferno, Canto 33, line 49. Count Ugolino is telling the Pilgrim about how he and his sons (or grandsons) were locked up in a tower and left to starve to death. Right before the line you quoted, Ugolino describes how they could hear the tower's door being sealed shut. While Ugolino's sons weep, he does not, saying that he has "turned to stone inside."
Two points here: first, Ugolino doesn't show any emotion at the impending doom of him and his children. He has no words to comfort, no prayers to offer; he simply sits in silence. This episode takes place in Cocytus, the frozen lake of circle nine that represents treachery and a lack of charity. More importantly, the notion of being turned into stone takes us back to the dramatic moment in Canto 9 when the furies called on Medusa to turn the Pilgrim into stone. Being turned to stone by Medusa represents despair, and the same allegorical imagery is at work here. This tie in makes the Eucharistic references several tercets later all the more poignant.
It is also not accidental that Ugolino goes blind in line 73 (just as the Pilgrim was blinded by Virgil in Canto 9). Stoniness and blindness is a motif that Dante works with a number of times in the Inferno.