Personalities of the Buddhist Suttas
DPPN: A brahmin. He once visited the Buddha at Sāvatthi and asked him whether the five sense-faculties (indriyāani), which were of different scope and range, had any commmon ground of resort (paṭi-saraṇa). [No citation given] The Buddha resplies that the mind is their common resort and, in answer to further questions, explains that there is nothing beyond Nibbāna; that the holy life has Nibbāna for its ending.
When the brahmin, greatly pleased with the Buddha's teaching, goes away, the Buddha tells the monks that Uṇṇābha has become an anāgamī and would, therefore, after death, no longer return to t his world.
[SN 5 51 15] records a visit of Uṇṇābha to Ānanda at Kosambī. He asks Ānanda what is the aim of holy life and, on being told that it is the abandoning of desire by means of jhāna, [not jhāna, but the 4 iddhipada] suggests that it would be a task without end. But Ānanda, by means of an illustration, explains how the task does come to an end, and Uṇṇābha expresses great satisfaction with the answer. Perhaps this refers to another brahmin of the same name.
[SN 5 51 15] is an important sutta in that it deals with the question that is frequently asked: "How can it be that desire is brought to an end with desire?"