Mr Smith came to see me. He said that he was upset about my behaviour. (we don't want to repeat Mr Smith)
When he is alone in his bedroom, Brian talks to himself all the time. (It is unnecessary to repeat Brian)
In English, pronouns only take the gender of the noun they replace in the 3rd person singular form. The 2nd person plural pronouns are identical to the 2nd person singular pronouns except for the reflexive pronoun.
The best thing is to memorize the following table.
AGREEMENT OF POSSESSIVE ADJECTIVES
In English, possessive adjectives change according to the gender and number of the possessor.
The boys have lost their books.
The student does his homework.
A dog wags its tail when it is happy.
The woman cleans her house.
Notice that the possessive adjective remains the same whether the thing possessed is singular or plural, masculine or feminine:
USE OF THE POSSESSIVE ADJECTIVES AND POSSESSIVE PRONOUNS:
Possessive adjectives always modify a noun so they must be used together with a noun:
Their table is made of wood.
You take care of your things.
Possessive pronouns do not modify a noun, they are independent of any other word in the sentence. They are used to replace possessive adjectives + nouns avoiding repetitions. Instead of saying:
"That car is my car." We say: "That car is mine."
Instead of saying:
"This book is her book. We say: "This book is hers."
THE "DOUBLE POSSESSIVE":
There is a pattern used with possessive pronouns, i.e.: of + possessive pronoun.
I saw a friend of mine (not "a friend of me"). A friend of mine/yours means "one of my friends/one of your friends".
A cousin of ours has just arrived from Birmingham.
Have you seen that new house of theirs?