For the record, it's not even possible to extract private keys from raw unsigned transactions because they are not contained in there. This is why it is possible for anybody to create a raw transaction that spends bitcoins from anybody's address, but as long as the user does not possess the private keys for those addresses, the user will not be able to sign the transaction and cannot broadcast (i.e. spend) it either.


This is a little misleading as those stolen transactions could be stolen again by other people, and then again and again, destroying the Bitcoin network in the process. It's not a "central party steals all the bitcoins for themselves" kind of thing.