Ilya has the second-to-last word in the novel, pre-epilogue. "Drink some water," he says. We know this isn't the most exciting line (although hydration is always a good idea, y'all), but they occur just before Raskolnikov finally turns himself in.
We aren't exactly sure why Raskolnikov decides to confess to Ilya. Perhaps it's because Ilya was the only cop to whom he really hadn't already confessed.