This post starts out positing a very unnatural case, and then goes on to restrict it in a way that makes it somewhat more natural. Let's start out with the unnatural idea:
Consider a case for subjects or objects, that makes the noun fail to fill the subject or object case slot. This leads to the transitivity of the verb failing to be what it's expected to be, and in the "unabsolutive" version, an ergative subject is demoted to absolutive. In the unnominative version, a direct object cannot be direct object any longer due to lack of a subject, and is thus marked nominative instead of accusative.
Now, this might seem like an odd case indeed - why would a case appear which simply serves to confound marking? And don't we already have oblique subjects with passives, and oblique objects with antipassives which cause exactly this with some voice marking thrown in for good measure?
Well, sort of. But let's create a situation where this situation could exist: certain nouns might lack the usual nominative or absolutive, and instead be some kind of 'pseudonouns' - perhaps instead of nominative/absolutive, their unmarked form looks morphologically like an adverb of some type. These pseudonouns' unmarked form is the unnominative/unabsolutive.
So, we might get a situation like the two examples below, one accusative example, one ergative example:
rain.UNNOM I.NOM soaked(1sg): the rain soaked me / I got soaked in the rain
I.abs sing(1sg, intrans) song.UNABS: I sing a song
Maybe these nouns have other case forms, just not nominative / absolutive - although I'd bet they're also likely to lack accusative or ergative as well. In a more congruence-based verb-centered language, maybe these morphologically look like adverbs and fail to take congruence (and make the congruence unlike it would usually be, i.e. objects become subjects, or transitive subjects become intransitive ones).
I am tempted to give Sargaĺk a few unnominative nouns, whose effect is only visible with ditransitive verbs: the subject and one of the objects then are nominative, with the other object being unnominative. I still think the Sargaĺk verb will be marked as ditransitive in that situation, though. Nouns referring to certain environmental things - the sea, rain, wind, sun, snow, foliage and the forest are the most likely to be antinominatives in Sargaĺk.