Imagine a language with a long-lasting split-ergative system, split by person rather than by TAM. (This, for the record, is common in Australia.) Unusually, for such a language, it has unique forms for all of nominative, accusative, ergative and absolutive. Now, the following system obtains in the language:
subj obj case alignment I reflexive ergative II ergative III ergative II I nominative reflexive ergative III ergative III I nominative II nominative reflexive absolutive IIIother ergative
The earlier system of congruence was eroded by a sound change that just so happened to lop off the verbal morphemes entirely (but the nominal morphemes survived by virtue of not having any sounds subject to that change). The new verbal congruence appears from present active participles, that have case congruence with their subject. Thus, the first person morpheme is identical to the ergative case suffix; the second person verb is unmarked, as is the third person verb.
The reflexive forms are somewhat special - the verb itself has no weirdness in the first person, just a first person object, with maybe a reflexive pronominal morpheme added, much like 'myself'. In the second person, the verb agrees with the subject, but in the third person, the reflexive participle agrees with the absolutive of the object.