Consider a language with possessive suffixes as well as an additional, lightly similar thing. We can imagine some interesting restrictions, though, and an immediate detour into that is called for about now.
In Proto-Finnic, the subject could not be marked with possessive suffixes; only the other cases permitted it. This is basically a nominative-alignment thing. Morphologically, this has left the trace that even subjects in Finnish, when marked by a possessive suffix, morphologically are identical to objects.
Now, the kind of suffix I am thinking of is an indirect object congruence marker. Thus, 'I gave a book to him' would come out as 'I gave book.[3sg ind. obj]'. Now, possessive and indirect object suffixes are in complementary distribution - they cannot cooccur.
However, we can imagine a weird situation where the indirect object congruence is permissible on intransitive subjects as well (at least for a short while, until the possessive marker catches up), for situations like 'the book is for him' and such.
For a short while, thus, the possessive marker would follow a nominative pattern, whereas the indirect object congruence marker would follow an ergative pattern.