Two elements of Nibbāna is mentioned at Iti 44. From this sutta, Theravada consider Nibbāna with residue (saupādisesā) is attained by an Arahant when he/she destroyed taints (asava) on his/her attainment of Arahantship, while Nibbāna without residue (anupādisesā) is attained when he/she died (Parinibbāna) without any aggregate left.
But when we read the sutta itself without any commentary, it seems that the sutta doesn’t say that Nibbāna without residue is the same as the experience of an Arhant when he/she died. Some people questioned this traditional interpretation and propose other explanation of Nibbāna without residue. For example, this article interpret Nibbāna without residue is the same as Nirodha Samāpatti.
So, when I discussed this topic with my friends, I came across a parallel of Iti 44 in Chinese Ekottarika Agama, i.e EA 16.2. Here I try to translate it freely (using Chinese lookup tools for SC site):
There are these two elements of Nibbāna . What it the two? Nibbāna element with residue and Nibbāna element without residue.
彼云 何名為有餘涅槃界？於是，比丘滅五下分 結，即彼般涅槃，不還來此世，是謂名為 有餘涅槃界。
What is called Nibbāna element with residue? Here, a monk, [by] destroying five lower fetters, he approached final Nibbāna [in Suddhavasa realm], not returning to this world. This is called Nibbāna element with residue.
彼云何名為無餘涅槃界？ 於 是，比丘盡有漏成無漏，意解脫、智慧解脫， 自身作證而自遊戲：生死已盡，梵行已立， 更不受有，如實知之，是謂為無餘涅 槃界。此二涅 槃界，當求方便，至無餘涅槃 界。如是，諸比丘！當作是學。」
What is called Nibbāna element without residue? Here, a monk destroyed taints (asava) and attained the unstained, is liberated in the mind (cetovimutti) and liberated by wisdom (paññāvimutti). He personally realized and penetrated for himself: ‘Birth and death has been destroyed, holy life has been established, there is no more experience of becoming.’ Thus he understands as it really is. This is called Nibbāna element without residue. These are two elements of Nibbāna, which should be sought with [exerting] effort, until [achieving] Nibbāna without residue. Thus, monks, you should train.
It’s remarkable that this sutra defined the two elements Nibbāna differently from Iti 44. It explained Nibbāna with residue as attainment of Anagami fuition which will lead attainment of final Nibbāna in the next life and Nibbāna without residue as attainment of Arahantship. I think this explanation is more make sense than explanation from Iti 44 because upādi is fuel of attachment which still have to be destroyed by Anagami and Arahant is not having it again.
What do you think, guys? Perhaps, is there other explanation of this two elements of Nibbāna from other Northern Buddhist sources?