I was asked this by a non-native speaker of English, and it's flummoxed me! Can you shed any light?
I said (automatically) that I would say "If you want to borrow that dress of X's, it's hanging on the wardrobe door."
But in most other languages possession is just the something of somebody ie. the pen of my aunt. I had to agree so, in that case it would be "If you want to borrow that dress of X, it's hanging on the wardrobe door." But that just doesn't sound right to me.