'Upapajjati' is for the most part found in suttas about results of kamma. It was also mentioned how it is found in the Appassuta Sutta (AN 4.6) about "progression" in learning/study.
'Uppajjati' is found unrelated to results kamma, most commonly as:
Eye consciousness arises dependent on the eye and sights.
Cakkhuñca paṭicca rūpe ca uppajjati cakkhuviññāṇaṃ
Interestingly both words are found in the one place in MN 148:
If anyone says, ‘the eye is self,’ that is not tenable (12).
‘Cakkhu attā’ti yo vadeyya taṃ na upapajjati.
The arising and vanishing of the eye is evident,
Cakkhussa uppādopi vayopi paññāyati.
so it would follow that one’s self arises (13) and vanishes (14).
Yassa kho pana uppādopi vayopi paññāyati, ‘attā me uppajjati ca veti cā’ti iccassa evamāgataṃ hoti.
That’s why it’s not tenable to claim that
Tasmā taṃ na upapajjati:
the eye is self.
‘cakkhu attā’ti yo vadeyya.
So the eye is not self
Piya Tan comments however appears to dispute the use of 'uppajjati' at 13:
12 “This is not fitting,” taṁ na upapajjati (lit “this does not arise”), but here Comy glosses as na yujjati, ‘it is not applicable; this is not the case/meaning” (MA 5:100).
13 “Rises,” upapajjati (PTS has uppajjati, which is erroneous), normally means “he reappears, is reborn,” but also has a
special usage in logic to mean, “to be tenable, to be acceptable,” as
it does here. (M:ÑB 1362 n1330)
14 “Passes away,” veti (from vi + √I, “to go” eti) (Skt vyeti), “he goes away, disappears, wanes” (M 3:282; S3:135; A 2:51; J 3:154). Comy
glosses as vigacchati nirujjhati (“he disappears, ceases”) (MA
I disagree with Piya Tan's dispute about "uppajjati" at 13 and agree with the answer of Guru Andrei Volkov, from which I have concluded "upapajjati" to mean: "follows" or "proceeds" or "progresses".
Thus, to me, it means:
If anyone says, ‘the eye is self,’ that does not follow/proceed/conclude [from that statement].
Because of undertaking such deeds, when their body breaks up, after death, they follow on/proceed into a place of loss, a bad place, the underworld,
So tena kammena evaṃ samattena evaṃ samādinnena kāyassa bhedā paraṃ maraṇā apāyaṃ duggatiṃ vinipātaṃ nirayaṃ upapajjati.
Little learning but follow to/proceed to the point of learning.
appassuto sutena upapanno
While not the words of the Buddha, MN 72 below:
But Master Gotama, when a mendicant’s mind is freed like this, where do they proceed to/go to?
Evaṃ vimuttacitto pana, bho gotama, bhikkhu kuhiṃ upapajjatī ti?
‘They proceed/they go’ doesn’t apply, Vaccha.
“Upapajjatīti kho, vaccha, na upeti”.
Well then, do they not proceed/not go anywhere?
Tena hi, bho gotama, na upapajjatī ti?
‘They don't proceed/don't go’ doesn’t apply, Vaccha.
“Na upapajjatīti kho, vaccha, na upeti”.
Woohoo! Buddha's reply in MN 72 explained below:
Tatrāpāhaṃ, bhikkhave, neva āgatiṃ vadāmi, na gatiṃ, na ṭhitiṃ, na cutiṃ, na upapattiṃ; appatiṭṭhaṃ, appavattaṃ, anārammaṇamevetaṃ.
Here, bhikkhus, I say there is no coming, no going, no staying, no deceasing, no uprising. Not fixed, not movable, it has no support. Just this is the end of suffering..