If you have any coin on loan at the time of a fork, you do not have it on balance and therefore you cannot receive coins on the corresponding chain.

Why not?
When someone borrows coins, they typically borrow them to sell immediately on the spot market to counterparties who cannot possibly be aware that the coins they bought came from someone who borrowed them. Spot traders unambiguously own their purchases, and are the rightful recipients of the coins on the corresponding chain and they can do with them what they like, whether that is selling them to others or taking them off of the platform entirely.

The terms of the loan dictate that you will receive the same number and type of coins you loaned within X days plus the agreed upon interest.

For context, you can read about the ETH/ETC fork.