According to usual understanding, the Proto-Uralic stem vowel contrast *-A | *-ə is still continued in the Mordvinic languages in nominals of the shape CVCV: word-finally *-A survives as a vowel (mostly *-ə, in some cases *-a), while *-ə is lost. This basic rule can be demonstrated easily enough. A particularly clean minimal pair is *pälä ‘half’ | *pälə ‘side’ (still conflated in UEW), with the contrast continued in three branches (and recall that *ä-ä > *a-ə in Finnic):
|Mordvinic||*päľä ‘half’||*päľ ‘side’|
|Mari||*pelə ‘half’||*pel ‘side’|
|Finnic||*pooli ‘half’||*peeli ‘side’|
Some more examples, including a second minimal pair *kerä | *kerə:
|*kämä > *kämə ‘boot’||*lämə > *ľäm ‘soup’|
|*enä > *ińə ‘big’||*sënə > *san ‘vein, sinew’|
|*puna > *pona ‘hair’||*unə > *on ‘sleep’|
|*kerä > *kiŕə ‘ball of yarn’||*kerə > *keŕ ‘bast’|
|*pesä > *pizə ‘nest’||*kusə > *koz ‘cough’|
|*ćëta > *śadə ‘100’||*kätə > *käď ‘hand’|
There appears to be one general exception to this however. I’ve given above examples after medial nasals, liquids and obstruents. But after medial semivowels, it seems that also original *-A is lost, presumably after reduction to *ə. Three cases with *-jA and one with *-wä are clear enough:
- Mk. /uj/ ‘brain’ << *ojwa ‘head’
- Er. /ki/ ‘moth’ << *käjä (via PMo *kij?)
- *koj ‘custom’ << *kuja
- Er. /kijov/ ‘snake’ << *kEjə-wä (*-ä per Nenets /śib́ă/ ~ /śiẃă/ < PSmy *kiwä)
(The other Mordvinic reflexes are more obscure. I’d presume development *kijəv > *kiju > /kju/, and lastly metathesis from this to produce the most widespread form /kuj/.)
A possible case with *-wa is *juv ‘chaff’ << ? *jowa ← Indo-Iranian *yawa-.  I suppose though that this could be also reconstructed as having been loaned as *jawə, followed by the early shift *a-ə > *o-a. The general vowel reduction *-a > *-ə also means that the development of secondary *-a is not actually directly evidenced in this stem type, and we could ask if the shift was not rather *a-ə > *o-ə. Still, lack of apocope in at least *ćalə > *ćola > *śulə ‘gut’ would seem to suggest that the stem vowel shift indeed extends to Mordvinic too, not just Samic.
Secondary apocope might moreover take place in *kuj ‘birch’ << ? *kojwa, not found as an independent word but probably continued in *kujmə ‘basket’ and Mk. /kujgeŕ/ ‘birch bark’. There is very little evidence to reconstruct *-a specifically, though; Finnic shows secondary *-u ~ *-o, the isolated Pite Sami word is probably loaned from Finnic, and Samoyedic *koəj (*kojə?) clearly does not indicate *-a. My suspicion is that this has rested only on the Mordvin /u/, given the older theory that *o-ə would generally give Mo. *o. But even starting from *kojwə, I would expect *-ə after an original consonant cluster *-jw- to resist primary apocope,  and to be instead lost after cluster simplification in the same wave of secondary apocope that targeted secondary *-ə from *-A.
— On the other hand, since *kuj- only occurs as a cranberry morpheme, maybe I have no reason to speak of apocope: this could be instead syncope, which appears to have operated in Mordvinic slightly more widely than apocope. Cf. e.g. *pizə-nə > *piznə > Er. /pizne/, Mk. /pizna/ as the diminutive of *pizə ‘nest’; *kajwa- → *kajwa-ma >> *kajmə ‘spade’,  *wajŋə → *wajŋə-ma >> *vajmə ‘spirit, breath’ as close equivalents to the derivation seen in ‘basket’. (I do not have examples of syncope in first members of compound readily available, however.)
Unreduced *-a does not seem to have been targeted by secondary syncope, per at least *kuja < ? *koja ‘fat’.
Lastly there seems to exist “tertiary” apocope after /al/. PU *-ala, *-ëla give /-al/ in modern Mordvinic; but Witsen‘s late 17th century vocabulary of Moksha still had ‹kala› ‘fish’ for modern /kal/ < *kala, as well as ‹sala› ‘thief’ < *sala (vs. no other unexpected final vowels). This seems regular enough too, though I have no idea what the motivation for such an oddly specific sound change could have been.
Nominals of the shape *CVjə, *CVvə can occur in Mordvinic, but all old native cases seem to come about by the lenition of earlier *p or *k. They probably still had medial obstruents at the time of secondary apocope. (Theoretically also examples with *j, *v from *ŋ or *x might exist.)
- *kopa > *kobə > *kuvə ‘bark’
- *śepä > *śebə > *śivə ‘collar’
- *jekä > *jegə > *ijə ‘year’
- *śekä > *śegə > *śijə ‘catfish, burbot’
- *tika > *tugə > *tuvə ‘pig’ (> Er. /tuvo/, Mk. /tuva/)
(If cognate with Finnic *cika < *tika; I have some doubts about this comparison.)
An early loanword example of this type is *Ravə ‘Volga’ ← Iranian *Rahā, probably loaned as intermediate *Raɣə. (UEW’s comparison with Khanty *răwV ‘mud’ seems far-fetched, and the reconstruction with *ŋ completely unmotivated.)
There are other proposed etymologies too that would seem to show secondary apocope of *-A > *-ə. Several of these however look dubious in various ways:
- ⁽*⁾oš ‘town’ ? < *woča ‘fence’
— There are no regular correspondences whatsoever between Mordvinic and PU here! The expected reflex would be **učə. Probably an incorrect etymology; words for ‘town’ can come from ‘fence’ (thus so already in Ob-Ugric), but they don’t have to do so.
- Mk. /luv/ in /käďluv/ ‘gap between fingers’ ? < *loma ‘gap’
— Maybe better compared with Finnic *lovi : *lovë- ‘cleft, gap’ (this has been passingly suggested by Aikio) or taken as a semantic specialization of /luv/ ‘number, order, etc.’ < *lukə (thus Grünthal 2012). I wonder if the Mordvins by any chance finger-count by gaps rather than fingers themselves?
- *čoŋ ‘foam’ ? < *čiŋa
— Finnic *hiiva ‘yeast’ with unexplained long *ii seems likely to be unrelated (and has a loan etymology from Baltic *šīvas ‘gray’). A proto-form for just Mari and Mordvinic could be rather reconstructed as *šoŋə, or maybe one is simply a loan from the other.
- *toŋ ‘kernel’ ? < *tuŋa
— Perhaps better reconstructed as *tuŋə. There is zero other evidence for *ŋ > *m in Finnic, and *tuma ~ *tuuma, if related, could represent a derivative *tuŋ-ma (or even later *tuw-ma with *wm > m explaining the Finnish variant with a short vowel?) The morphology of this would be obscure though, *-ma usually forms only deverbal and locative nouns.
At least one seemingly unimpeachable case remains that I have no explanation for: *ur ‘squirrel’ < *ora(-pa).
 Not from front-vocalic *jewä, as reflected in Finnic *jüvä ~ *jivä, but rather a parallel loan. While this difference seems obvious, I think Holopainen 2019 is probably be the first major source to state this explicitly?
 The closest parallels for this kind of retention of *ə are *veťə ‘5’, *kotə ‘6’, where *ť/t are probably from earlier clusters (not necessarily traditionally assumed *tt, however), and PU *-ə is clearly indicated by Finnic and Samic.
 Misglossed in Uralonet as ‘to scoop’; the word is a noun, not a verb.