1) Intransitive verbs turn pseudo-transitive, possessor into pseudo-subject
The possessor turns into a pseudo-subject with which the verb agrees, the possessum retains subject marking (but does not trigger congruence on the verb). The possessum is head-marked for possession. There's a slight probability for explicit object marking on such possessums, despite their essentially being intransitive subjects. The possessor may be marked with the secondary subject marking.
2) Possessor to the left of the possessum
The possessum has the possessum-marking, the case marking on the possessor is somewhat arbitrary. Proper nouns tend to be nominative, some nouns have a preferrence for some case, but this 'preferrence' goes both ways - both the possessor and possessee nouns may affect which case will be used. Some amount of displacement for the possessor is also possible - the fewer the arguments in the clause, the more likely such a displacement is. Such displacement is generally at most a word or two in some direction - or to sentence-initial position. The possessor should not interact syntactically with anything else, such as adpositions or anything.
3) Possessum carries possessum-marking, no obvious possessor
In a sentence with multiple arguments, there is a hierarchy:
subject > indirect object > instrumental = direct object > locatives > other obliquesIf a noun that is instrumental in the sentence has possessum marking, it can be owned by an indirect object or a subject (even a pro-dropped subject is eligible). Likewise, locations can be owned by the direct object, the instrumental etc. A subject can be owned by a direct object, however, or by a subject or object of the previous clause. The subject, and direct and indirect objects of a matrix clause are the only constituents that can be owners of any argument of a subordinate clause. Naturally, the likelihood that the owner is high up in the hierarchy is also rather large - and gendered pronouns may be added to help disambiguate. These generally are in the dative case. The presence of such a pronoun generally removes the chance that the possessor is the subject as well. Definiteness (and demonstrative adjectives) increases the likelihood that a noun is the possessor. Secondary subjectness and reciprocal objectness may also affect the likelihood that some noun is the possessor (i.e. 2nd subjectness increases the likelihood for a non-subject to be the owenr, reciprocal object marking increases the likelihood that a noun that syntactically is in the same position is the owner, i.e. a noun that is also coordinated with its possessum.)
Thus, reflexive possession - although with a slight ambiguity as to which "higher up" noun is the possessor - is the default assumption in Bryatesle. Non-reflexive possession generally is obtained by extra pronouns.
4) First and Second Person Pronouns
The first and second person have possessive forms of their pronouns.
1 sg nereThe -e part marks congruence for nominative masculine singular marker, and is replaced with the adjectival congruence markers for the relevant case. The possessive pronoun goes after its head noun. Third person forms masc: mezer, fem: ezer, neut: syn appear in some dialects a few centuries after the form of Bryatesle that I have primarily described. These do not trigger the presence of head marking. However, use of them is quite infrequent, as other strategies are preferred, especially whenever a first or second person subject is involved.
2 sg tere
1 pl vele
2 pl xene