The Buddha describes four sorts of persons in relationship to the sorts of yokes to rebirth [saŋyogana] they have or have not yet got rid of.
Read the Sutta
Index to available translations: AN 4.131
This sutta raises important issues.
First is an unusual breakdown of the saŋyoganas:
1. those yoking one to rebirth in the lower worlds (Woodward translates 'this World' and then, for the Once Returner translates in a way that can be misunderstood as indicating that he has not broken any of the first five fetters (this, apparently, an opinion derived from commentary)). But these are yokes to any 'kama-loka' which includes the deva-worlds up to the Tusita Realm see the Buddhist cosmology here
These first five yokes are:
1. The own-body or, the one-truth view (see below for an explanation)
2. Doubt about kamma, the Awakening of the Buddha, etc.,
3. Belief that good deeds, ethical conduct or rituals can bring an end to Pain,
4. Wishing for pleasure,
5. Deviant thinking.
When the first three of these are broken by the Streamwinner, he is no longer subject to rebirth lower than the world of humans. He is able to see when he is hanging on to a way of viewing his individuality that will lead him to hell or some other low state and is able to let that go without having the strength to let go of every sort of being.
The Once-returner is also a Streamwinner, so he will have at least broken the first three yokes.
The Buddha is in this case speaking of the category as a whole, not it's individual components. He does not say 'has not broken any fetters' he says 'has not broken the 'orambhāgiyāni saŋyojanāni.' All five.
2. those yoking one to rebirth
3. those yoking one to existence.
Bhkkhu Bodhi cites the commentary for definition of the last two and the result is a restatement of the terms with nothing informative added.
You are welcome to disagree, but I suggest we do not need to go off into bizarre speculations relying on the commentary to understand these last two categories.
It is sufficient to carefully examine the nature of the 10 saŋyojanāni that we are given.
First, to understand the latter two categories, one must understand fetter #1: sakkāyaditthi. The usual understanding is that this means 'view of self' understanding that to mean the idea one has that one has an eternal self, etc.
Actually the usual understanding of how this yoke is broken is to flip to the incorrect view that there is no self which is why this yoke must be understood in broader terms than 'own-self'.
The emphasis should be on the 'view' part of the compound. The holding onto points of view concerning individuality with the idea: 'This alone is the truth, all other views are stupidity.'
The Streamwinner who has freed himself from this yoke will have understood that the problem of pain arises as a result of the holding on to a view concerning his having an eternal self, but he will not necessarily have actually abandoned the identification, thoughts, and so forth that arise from having had that point of view in the past.
Its like the phantom limb phenomena.
He is likened to the person who has come across a well without a bucket to retrieve the water. [see SN 2.12.68] He can see the solution (as it were) but has not got the means to drink.
In a similar way all the first five fetters have to do with orienting the intellect to the goal and focusing the individual's behavior on elimination of various gross obstructions to perception of his inner workings.
These first five do not constitute having uprooted the underlying drive to be.
The next two fetters are lust for form and lust for immaterial existence: the underlying drives to be, aka: yokes to actual rebirth.
The final three yokes are pride,
and being subject to misunderstanding (aka blindness).
Here we have the case of the person who has sufficient experience to prevent him from behavior that would result in rebirth in any realm of being, but for whatever reason (long habit, experience, difficult circumstances) there remain these subtle states of mind.
This is the case of the Non-Returner who no longer own-makes (sankharams) and who obtains final release at some point after the death of the body but before assuming any rebirth.
There is much discussion back and forth concerning the precise state this individual is in caused by trying to imagine a state of existence which does not require rebirth. A between-births. But this is not necessary if one examines AN 11.7 and similar suttas where it is stated that there is the possibility of perception without perception of 'being' in any realm of 'being'.
'Existence' is a matter of perception, rebirth is a matter of having acted upon perception to the effect of having set rolling identification with form or the formless.
The Paṭicca Samuppada differentiates between bhava and jāti: existence and rebirth. This person is percipient of these subtle mental states. That is what remains for him of existence. That is what he gets rid of, without assuming rebirth, to become Arahant.