Does SafeCoin work on a blockchain? How does the network verify transactions and who owns which coin?
No it doesn’t. Information about the way safecoin works can be found here: http://maidsafe.net/SystemDocs/user_perspective/safecoin.html
But applications can be built on top of maidsafe that makes ledger banking possible.
example: safecoins are transfered to a feeding address, and the same amount of ledgercoin is given out in return. At any point any ledgercoin can be traded for a safecoin. This would create a parallel system where fraud protection, hacking protection etc. can be provided as long as you can trust the bank.