As is well-known, intransitive deponent verbs can enter into Ablative Absolute constructions (e.g., Cicerone mortuo, Cicerone nato, etc.) and in (other) dominant participle constructions (e.g., ante Ciceronem mortuum, ante Christum natum, etc.). However, some intransitive non-deponent verbs can also be found in these constructions (e.g., sole occaso, ante solem occasum, etc.).
Putting transitive verbs aside (e.g., cf. Carthagine deleta, post urbem conditam, etc.), I was wondering which is the specific grammatical set/class of intransitive verbs that can enter into these participial constructions. As for Romance languages it seems to be the case that so-called "unaccusative verbs" can typically enter into absolute participle constructions: e.g., Cat. Mort Ciceró,...; Vingudes les pluges..., etc. Cf. also Sp. Muerto Cicerón, ...; Llegadas las lluvias,..., etc. However, Latin appears to make a different cut since unaccusative verbs like intr. venire cannot form AA constructions (e.g., *Imbribus ventis, ...) nor other dominant participle constructions (e.g., *post imbres ventas).
So I was wondering if there is any linguistic generalization in Latin as for which type of intransitive verbs are allowed to enter into Ablative Absolute constructions and into (other) dominant participle constructions.