I would make a few points:
First, suttacentral gives SA 961 and SA2 195 as parallels to this sutta. As far as I can tell neither of these are parallels at all, perhaps @cdpatton can confirm?
Second, @sujato 's translation of atthattā as “self survives”, while a massive improvement on his earlier “the self exists in an absolute sense”, is still quite clearly taking a strong position in relation to the meaning or intention of the sutta, one that obscures rather than illuminates the ambiguities and potential philosophical controversies that do indeed surround it.
Third, @Sunyo 's insistence that the annihilationist position was that a real, existent, substantial self or atta was annhiliated, while consistent with Theravada orthodoxy and obviously vitally important to maintaining certain readings of the annata doctrine, is profoundly difficult, at least for me, to see on the basis of the primary canonical description given in the suttas:
One time, sir, I approached Ajita Kesakambala and exchanged greetings with him. Ekamidāhaṁ, bhante, samayaṁ yena ajito kesakambalo tenupasaṅkamiṁ; upasaṅkamitvā ajitena kesakambalena saddhiṁ sammodiṁ. When the greetings and polite conversation were over, I sat down to one side, and asked him the same question. Sammodanīyaṁ kathaṁ sāraṇīyaṁ vītisāretvā ekamantaṁ nisīdiṁ. Ekamantaṁ nisinno kho ahaṁ, bhante, ajitaṁ kesakambalaṁ etadavocaṁ: ‘yathā nu kho imāni, bho ajita, puthusippāyatanāni …pe… sakkā nu kho, bho ajita, evameva diṭṭheva dhamme sandiṭṭhikaṁ sāmaññaphalaṁ paññapetun’ti?
He said:
Evaṁ vutte, bhante, ajito kesakambalo maṁ etadavoca:‘Great king, there is no meaning in giving, sacrifice, or offerings. There’s no fruit or result of good and bad deeds. There’s no afterlife. There’s no such thing as mother and father, or beings that are reborn spontaneously. And there’s no ascetic or brahmin who is well attained and practiced, and who describes the afterlife after realizing it with their own insight. The denial of “mother and father” is usually interpreted as the denial of moral duty towards ones’ parents. However, I think it is a doctrine of conception which denies that a child is produced by the mother and father. Rather, the child is produced by the four elements, with parents as mere instigators and incubators.
‘natthi, mahārāja, dinnaṁ, natthi yiṭṭhaṁ, natthi hutaṁ, natthi sukatadukkaṭānaṁ kammānaṁ phalaṁ vipāko, natthi ayaṁ loko, natthi paro loko, natthi mātā, natthi pitā, natthi sattā opapātikā, natthi loke samaṇabrāhmaṇā sammaggatā sammāpaṭipannā, ye imañca lokaṁ parañca lokaṁ sayaṁ abhiññā sacchikatvā pavedenti.This person is made up of the four primary elements. When they die, the earth in their body merges and coalesces with the main mass of earth. The water in their body merges and coalesces with the main mass of water. The fire in their body merges and coalesces with the main mass of fire. The air in their body merges and coalesces with the main mass of air. The faculties are transferred to space. This is a materialist analysis of the person.
Cātumahābhūtiko ayaṁ puriso, yadā kālaṁ karoti, pathavī pathavikāyaṁ anupeti anupagacchati, āpo āpokāyaṁ anupeti anupagacchati, tejo tejokāyaṁ anupeti anupagacchati, vāyo vāyokāyaṁ anupeti anupagacchati, ākāsaṁ indriyāni saṅkamanti.Four men with a bier carry away the corpse.
Āsandipañcamā purisā mataṁ ādāya gacchanti.Their footprints show the way to the cemetery.
Yāvāḷāhanā padāni paññāyanti.The bones become bleached. Offerings dedicated to the gods end in ashes.
Kāpotakāni aṭṭhīni bhavanti, bhassantā āhutiyo.Giving is a doctrine of morons.
Dattupaññattaṁ yadidaṁ dānaṁ.When anyone affirms a positive teaching it’s just hollow, false nonsense.
Tesaṁ tucchaṁ musā vilāpo ye keci atthikavādaṁ vadanti.Both the foolish and the astute are annihilated and destroyed when their body breaks up, and don’t exist after death.’
Bāle ca paṇḍite ca kāyassa bhedā ucchijjanti vinassanti, na honti paraṁ maraṇā’ti.And so, when I asked Ajita Kesakambala about the fruits of the ascetic life apparent in the present life, he answered with the doctrine of annihilationism.
Itthaṁ kho me, bhante, ajito kesakambalo sandiṭṭhikaṁ sāmaññaphalaṁ puṭṭho samāno ucchedaṁ byākāsi.
What part of the above is suggestive of, or even compatible with, a philosophy of a real existent atta that is destroyed at death? It seems to me that the only reason for that gloss is that without it we have something that looks almost exactly like anatta, as some Theravadins would posit that doctrine.
Fourth, the context of SN44.10 is the undeclared points, which are absolutely not confined to “atta” questions, and as I have said elsewhere are discussed in much greater detail in other suttas, notably MN72 in ways that make the idea that the undeclared points are really about anatta completely untenable.
Anyway, I know am unlikely to be persuasive to many on here steeped in Theravada tradition, but I think it is a shame that so few people take an interest in the undeclared points outside of the anatta context, as I think it is in fact the gateway to the real penetration of what Buddhism was about for the Buddha and his immediate followers.
Metta.