What other ways can this be phrased? This doesn't even sound right to me. How do you put a possessive-passive sentence properly. Quite confused for some reason.
"This [thing] of mine/his/hers/theirs/yours/ours" is perfectly normal and acceptable. There is nothing "not right" about it.
Possessives with of
Noun phrase + of + possessive pronoun
We can talk about possession using the pattern: noun phrase + of + possessive pronoun:
A friend of mine told me that all of the tickets have already sold out.
Where’s Martin? He’s gone to pick up a cousin of his at the station.
Is Linda McGrath a close friend of yours?