The last reference to Sanjaya is in the Ashramavasika Parva of the Mahabharata. As I discuss in this answer, Dhritarashtra, Gandhari, Kunti, Vidura, and Sanjaya all left Hastinapura and went to Vyasa's Ashram to become Sanyasis. Vidura died there, and after that the rest of them decided to go to Gangadwara, which is modern-day Haridwar, and engage in Tapasya on the Ganga river. One day, there was a forest fire, which Dhritarashtra, Gandhari, and Kunti chose to be consumed by, since fire is a fitting death for a Sanyasi. But on Dhritarashtra's instruction Sanjaya escaped the fire, as described by Narada in this chapter of the Ashramavasika Parva of the Mahabharata:
The king, seeing the conflagration approach him from all sides, addressed the Suta Sanjaya, that foremost of skilful charioteers, saying,--'Go, O Sanjaya, to such a place where the fire may not burn thee. As regards ourselves, we shall suffer our bodies to be destroyed by this fire and attain to the highest goal.' Unto him, Sanjaya, that foremost of speakers, said,--'O king, this death, brought on by a fire that is not sacred, will prove calamitous to thee. I do not, however, see any means by which thou canst escape from this conflagration. That which should next be done should be indicated by thee.'
Thus addressed by Sanjaya the king once more said,--'This death cannot be calamitous to us, for we have left our home of our own accord. Water, fire, wind, and abstention from food, (as means of death), are laudable for ascetics. Do thou, therefore, leave us, O Sanjaya, without any delay. Having said these words to Sanjaya, the king concentrated his mind. Facing the east, he sat down, with Gandhari and Kunti. Beholding him in that attitude, Sanjaya walked round him. Endued with intelligence, Sanjaya said,--'Do thou concentrate thy soul, O puissant one.' The son of a Rishi, and himself possessed of great wisdom, the king acted as he was told. Restraining all the senses, he remained like a post of wood. The highly blessed Gandhari, and thy mother Pritha too, remained in the same attitude. Then thy royal sire was overtaken by the forest-conflagration. Sanjaya, his minister, succeeded in escaping from that conflagration. I saw him on the banks of Ganga in the midst of ascetics. Endued with great energy and great intelligence, he bade them farewell and then started for the mountains of Himavat.
So the last bit of information we have about Sanjaya is that Narada saw him leaving Haridwar and heading for the Himalayas.