Good question. Perhaps this is a bit of a facetious response but what happens if you delete all the databases within your organisation?
... you lose all the data! Corda is no different. As such, you need to back up your data.
Corda could provide the possibility of restoring shared data from peers on the network but it's not something we have implemented yet.
If Corda nodes are presented with a valid transaction hash, they will respond with the transaction data corresponding to that hash. As such, if you record a list of tx hashes and the identities of the peers which you know to possess the corresponding transaction data, then in theory, you can recover all of your shared data. To me, it seems this should be seen as a "last resort" strategy to recovering your data.
As an aside, the value of DLT is in reducing/eliminating inconsistencies and thus the need to reconcile ledgers. Some have erroneously identified another "benefit" - that they now don't have to worry about data recovery or backups because the data is “on the ledger”. Crucially, this is only a valid benefit if your business depends only on shared data and has no private data of its own. Having said that, as Corda is designed to bring untrusting parties into consensus, you can never trust that your counter-party won't delete a state object, as such you should always keep your own backups.
If you do have private data, then of course you'll back up it as per usual and you may as well back up the shared data whilst you're at it!