Is this correct possessive pronoun?

My brother owes money and he refuses to pay back MINE (Possessive pronoun)

Yes. Both MY and MINE are possessive pronouns.

I don't think the second half of your sentence makes sense.

... he refuses to pay back ______.

The sentence here is better:
http://www.jiskha.com/display.cgi?id=1278523390

No, the possessive pronoun "mine" is not used correctly in this sentence. In English, the correct possessive pronoun to refer to something owned by the speaker is "mine." However, in this context, you should use the possessive pronoun "his" to match the subject of the sentence, which is "my brother."

So, the correct sentence would be: "My brother owes money and he refuses to pay back his."

If you want to learn more about possessive pronouns and how to use them correctly, you can refer to English grammar resources, such as grammar books, online grammar guides, or language learning websites. These resources can provide in-depth explanations and examples to help you better understand and use possessive pronouns in sentences.