I read on the internet:
Arahants have eliminated all Sankhara. So there is no need for accumulation of memory.
Have Arahants really eliminated all Sankhara?
Please answer with Pali sutta references.
In Udana 6.1, we see the Buddha having intentions and making plans for the afternoon - this showed that he still had mental formations, volition and intention as a living arahant. So, he still had sankhara.
I have heard that on one occasion the Blessed One was staying near Vesālī at the Gabled Hall in the Great Forest. Then, early in the morning, he adjusted his under robe and — carrying his bowl & robes — went into Vesālī for alms. Then, having gone for alms in Vesālī, after the meal, returning from his alms round, he addressed Ven. Ānanda, "Get a sitting cloth, Ānanda. We will go to the Pāvāla shrine for the day's abiding."
Responding, "As you say, lord," to the Blessed One, Ven. Ānanda followed along behind the Blessed One, carrying the sitting cloth. Then the Blessed One went to the Pāvāla shrine and, on arrival, sat down on the seat laid out.
Seated, the Blessed One addressed Ven. Ānanda, "Vesālī is refreshing, Ānanda. Refreshing, too, are the Udena shrine, the Gotamaka shrine, the Sattamba shrine, the ManySon shrine, the Sāranda shrine, the Pāvāla shrine.
So, living arahants still have sankhara. What they do not have is latent tendencies (anusaya), defilements (kilesa), effluents (asava), fetters (samyojana), craving (tanha) and clinging (upadana).
More precisely, living arahants have the aggregate of sankhara but not the clinging-aggregate of sankhara, because they have stopped clinging. See SN 22.48.
Also, Thanissaro Bhikkhu's commentary of Iti 44 implies that living arahants still have the five aggregates operating till physical death (sa-upadisesa), but there is no continuation of suffering from the point of their enlightenment.
SN 22.85 says Arahants have "sankhara":
“If, friend Yamaka, they were to ask you: ‘Friend Yamaka, when a bhikkhu is an arahant, one whose taints are destroyed, what happens to him with the breakup of the body, after death?’—being asked thus, what would you answer?”
“If they were to ask me this, friend, I would answer thus: ‘Friends, form is impermanent; what is impermanent is suffering; what is suffering has ceased and passed away. Feeling … Perception … Volitional formations … Consciousness is impermanent; what is impermanent is suffering; what is suffering has ceased and passed away.’ Being asked thus, friend, I would answer in such a way.”
“Good, good, friend Yamaka!
MN 43 says a living individual has ayu-sankhara (vitality/life force):
But because the life forces and the phenomena that are felt are different things, a mendicant who has attained the cessation of perception and feeling can emerge from it.
Yasmā ca kho, āvuso, aññe āyusaṅkhārā aññe vedaniyā dhammā, tasmā saññāvedayitanirodhaṃ samāpannassa bhikkhuno vuṭṭhānaṃ paññāyatī”ti.
When a mendicant has attained the cessation of perception and feeling, their physical, verbal, and mental processes have ceased and stilled. But their vitality is not spent; their warmth is not dissipated; and their faculties are very clear.
Yo cāyaṃ bhikkhu saññāvedayitanirodhaṃ samāpanno tassapi kāyasaṅkhārā niruddhā paṭippassaddhā, vacīsaṅkhārā niruddhā paṭippassaddhā, cittasaṅkhārā niruddhā paṭippassaddhā, āyu na parikkhīṇo, usmā avūpasantā, indriyāni vippasannāni.
MN 26 describes Nibbana as the "calming (samatho) of all sankhara" rather than "destruction of all sankhara":
It’s also hard for them to see this thing; that is, the stilling of all activities, the letting go of all attachments, the ending of craving, fading away, cessation, extinguishment.
Idampi kho ṭhānaṃ duddasaṃ yadidaṃ—sabbasaṅkhārasamatho sabbūpadhipaṭinissaggo taṇhākkhayo virāgo nirodho nibbānaṃ.
The arsing and decay of aggregates, including fabrications, do not disappear for an Arahat, as long as alive, but he is already detached from them, no more taking on them. The usual similar is that of the skin of a cow when patched on it's body again, after having been cut away.
For Such, only dukkha arises, when Dhammas do arising, and fades away, when Dhammas are fading.
[Note: This is a gift of Dhamma and not meant for commercial purpose or other low wordily gains by means of trade and exchange.]
Now from the remainderless fading & cessation of that very ignorance comes the cessation of fabrications.