user8157: I have not read 100% of the Pali suttas. I am only aware of the term "saupādisesā" in the following sutta: 

“Bhikkhus, there are these two Nibbāna-elements. What are the two? The Nibbāna-element with residue left and the Nibbāna-element with no
  residue left.
“What, bhikkhus, is the Nibbāna-element with residue/fuel (saupādisesā) left? Here a bhikkhu is an arahant, one whose taints are destroyed, the holy life
  fulfilled, who has done what had to be done, laid down the burden,
  attained the goal, destroyed the fetters of being, completely released
  through final knowledge. However, his five sense faculties remain
  unimpaired, by which he still experiences what is agreeable and
  disagreeable and feels pleasure and pain. It is the extinction of
  attachment, hate, and delusion in him that is called the
  Nibbāna-element with residue left.
*“Now what, bhikkhus, is the Nibbāna-element with no residue left? Here a bhikkhu is an arahant … completely released through final
  knowledge. For him, here in this very life, all that is felt/experienced (sabbavedayitāni), not being delighted in, will be become cold (siti). That, bhikkhus, is
  called the Nibbāna-element with no residue left.*
Iti 44

Based on the Pali suttas - without quoting any views of commentaries or scholars - what teachings exist in the Pali suttas that might explain the meaning of "Nibbāna-element with residue (saupādisesā) left"? 

user2282: The Suttas isn't a comprehensive system in the sense that it does not provide exhaustive definitions/explanations to every single term/concept. That's why we have the "TiPitaka", the "Three Baskets" instead of "Single Basket" of Suttas. Therefore one will have to rely on a "view" nevertheless (whether one's own view, others' view, or the Commentary's view, etc...) until attaining arahantship to verify things for oneself. Here's Ven. Bodhi's note from "Connected Discourse" citing Comy's explanation:

in relation to Nibbana, it denotes the five aggregates, which persist until the arahant expires. Nibbana as experienced by the arahant during life is called the saupadisesanibbanadhatu , "the Nibbana element with a residue (= the five aggregates) remaining"; as attained at his death it is the anupadisesanibbanadhatu, "the Nibbana element without residue remaining."


8157: <p>I have not read 100% of the Pali suttas. I am only aware of the term "saupādisesā" in the following sutta: </p>

<blockquote>
  <p><em>“Bhikkhus, there are these two Nibbāna-elements. What are the two? The Nibbāna-element with residue left and the Nibbāna-element with no
  residue left.</em></p>
  
  <p><em>“What, bhikkhus, is the Nibbāna-element <strong>with residue/fuel (saupādisesā)</strong> left? Here a bhikkhu is an arahant, one whose taints are destroyed, the holy life
  fulfilled, who has done what had to be done, laid down the burden,
  attained the goal, destroyed the fetters of being, completely released
  through final knowledge. However, his five sense faculties remain
  unimpaired, by which he still experiences what is agreeable and
  disagreeable and feels pleasure and pain. It is the extinction of
  attachment, hate, and delusion in him that is called the
  Nibbāna-element with residue left.</em></p>
  
  <p>*“Now what, bhikkhus, is the Nibbāna-element with no residue left? Here a bhikkhu is an arahant … completely released through final
  knowledge. For him, here in this very life, all that is felt/experienced (<em>sabbavedayitāni</em>), not being delighted in, will be become cold (siti). That, bhikkhus, is
  called the Nibbāna-element with no residue left.*</p>
  
  <p><a href="https://suttacentral.net/iti44/en/ireland" rel="nofollow noreferrer"><em>Iti 44</em></a></p>
</blockquote>

<p>Based on the Pali suttas - without quoting any views of commentaries or scholars - what teachings exist in the Pali suttas that might explain the meaning of "<em>Nibbāna-element with residue (saupādisesā) left</em>"? </p>
 2282: <p>The Suttas isn't a comprehensive system in the sense that it does not provide exhaustive definitions/explanations to every single term/concept. That's why we have the "TiPitaka", the "Three Baskets" instead of "Single Basket" of Suttas. Therefore one will have to rely on a "view" nevertheless (whether one's own view, others' view, or the Commentary's view, etc...) until attaining arahantship to verify things for oneself. Here's Ven. Bodhi's note from "Connected Discourse" citing Comy's explanation:</p>

<blockquote>
  <p>in relation to Nibbana, it denotes the five aggregates, which persist until the arahant expires. Nibbana as experienced by the arahant during life is called the saupadisesanibbanadhatu , "the Nibbana element with a residue (= the five aggregates) remaining"; as attained at his death it is the anupadisesanibbanadhatu, "the Nibbana element without residue remaining."</p>
</blockquote>
