From my reading of the whitepaper, the protocol forces the data to be replicated by scrambling it with the miner's public key. It's not possible to have two identities using the same backing storage. However, two identities could use the same account or even the same disk, in which case the data would be replicated on that disk, which is useless. At the same time, there is no benefit to the miner to doing things that way.

As far as "running away", the miner is paid by the network for proving they are storing some data at a certain time. It's not like a storage contract for someone's individual data paid up front.