These are both fine and common: I have the money which was loaned to you. I have the money loaned to you. The second one below I have heard frequently also, so I would consider it informally OK at least.
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AnonymousHe had a voice would raise the rafters!It strikes me as British as well. It's very uncommon in North America to leave out a 'who', 'which', or 'that' which is the subject of its relative clause.