Phassanirodho

When the six sense fields fade away and cease with nothing left over, contact ceases.

Channaṃ tveva, phagguna, phassāyatanānaṃ asesavirāganirodhā phassanirodho;

SN12. 2 12

“When the six sense fields fade away and cease with nothing left over” is this via jhānas?

Yes and no. Jhanas contribute to this but cannot be totally explained by the Jhanas alone, as some degree of perception remains, even in the 8th jhana which defined as hardly having any perception, but not having non-perception (neva sanna an nasanna?). The Buddha as a bodhisattva learnt it under a teacher but didn’t consider it the total cessation of suffering. It contained a slight perceptual element which means it is subject to arising and passing away, which in our is unsatisfactory, which in turn is not self. Continuously watch these three characteristics (taking the sign of these, that is) is developing vipassana and Insight (yatabhuta nana) that arises leads to repulsion, dispassion and cessation (nirodha). This cessation it seems to me is cessation of contact (phassanirodha). Sila, samadhi and Panna are required for this to happen.

With metta

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I will try to avoid the indigestible soup of putting everything in the same pot, and curb my frame of reflexion to the mere components of your question - sticking as much as I can, to the fields of sense (ayatana) :

“When the six sense fields fade away and cease with nothing left over” is this via jhānas ?”, you ask.

The original question in SN 12.2 is:
Venerable sir, who makes contact?”
“Not a valid question,” the Blessed One replied. “I do not say, ‘One makes contact.’…
… I do not speak thus. Since I do not speak thus, if one should ask me, ‘Venerable sir, with what as
condition does contact come to be?’ this would be a valid question. To this the valid answer is: ‘With the six internal fields of sensory experience as condition, contact comes to be;
with contact as condition, feeling.’”

“”"
Contact through the eye, ear, nose, tongue, body, and mind.
cakkhusamphasso,… manosamphasso.
(the six internal fields of sensory experience).

One does not make contact.
It is with the six internal fields of sensory experience, as condition, that contact comes to be.

What are these six internal fields of sensory experience (ajjhatikkani ayatanani) ?
Read this first: SENSE-EXPERIENCE in Genuine Buddhism ( from Texts common to Early Buddhist schools )  ________ .... - JustPaste.it
Then the notes on ayatana at the bottom of this page: * - JustPaste.it

Now, what is said about jhana’s requirement ?
Jhāna (from jhāyati) - Sanskrit: kṣāyati, from √ क्षि kṣi - to make an end of (RV. AV. MBh.)
See jhana- JHANA (All the Suttas’ extracts below, have parallels in Chinese, and/or Tibetan, and/or Sanskri... - JustPaste.it

The first jhana is, among other things, about making an end of the sensual pleasure, through seclusion (vivicceva kāmehi).
See Viveka - VIVEKA Discrimination / Separation / Seclusion  ________ . Note: Viveka has always had the meani... - JustPaste.it).
Viveka is discrimination between the external and the internal - separation from the external - and seclusion in the internal.
This is a requirement, and the process as well, of the first jhana.

One doesn’t need to cross legs and do the all shebang of “deep absorption” to do jhana, at this level.

One should just restrain the indriya(ni). That is how one perfects and completes the seclusion (viveka) . This is how the six internal fields of sensory experience come to fade away.
However, in your question, it is said that “the six internal fields of senses should also” cease with nothing left over".
Going back to the link provided above on jhana, you can see that this does happen in the fifth jhana. (explained here * - JustPaste.it - in blue at the bottom of the page - Note also that, in previous threads, I have already suggested that perception/sanna has also the underlying meaning of “inquiry and its assumptions”, in the Vedic texts).

Simple, isn’t it ?
Maybe a bit hard to understand within a Lockean or Humean frame of mind. But not for Kantian or Cartesian ones, for instance.
In other words, you can advance (or retreat and escape, ) through non-sensory spheres (in higher jhanas). For everything is not just senses in Buddhism; as in Descartes, Kant, Hegel, etc…

Metta

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“But from the complete fading away and cessation of ignorance, there is the cessation of volitional processes, from the cessation of volitional processes, the cessation of consciousness, from the cessation of consciousness, the cessation of mind and body, from the cessation of mind and body, the cessation of the six sense spheres, from the cessation of the six sense spheres, the cessation of contact, from the cessation of contact, the cessation of feeling, from the cessation of feeling, the cessation of craving, from the cessation of craving, the cessation of attachment, from the cessation of attachment, the cessation of continuation, from the cessation of continuation, the cessation of birth, from the cessation of birth, old age, death, grief, lamentation, pain, sorrow, and despair all cease, and so there is a cessation of this whole mass of suffering.”SuttaCentral

Cessation of all contact is Nibbāna

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“Therefore, monks, that dimension should be experienced where the eye ceases and the perception of form fades. That dimension should be experienced where the ear ceases and the perception of sound fades. That dimension should be experienced where the nose ceases and the perception of aroma fades. That dimension should be experienced where the tongue ceases and the perception of flavor fades. That dimension should be experienced where the body ceases and the perception of tactile sensation fades. That dimension should be experienced where the intellect ceases and the perception of idea fades. That dimension should be experienced.”SuttaCentral