Stealing never transfers legal ownership. I assume what you are actually asking is whether a thief could successfully cash out stolen stock certificates. To that, the answer is not easily.
All changes in ownership of stock shares have to be registered with the transfer agent for the stock. When you present physical share certificates to a broker for sale, the broker will verify the validity of the certificate with the transfer agent. If the certificates have been reported stolen, all transfers would be blocked. Certificates do have a form for transferring ownership printed on the back, so if they hadn't been reported stolen yet, you could fill out that form and claim that you had bought or been given the certificate by the registered owner. However, you'd have to forge the signatures, and find a corrupt notary, willing to perjure themselves, to attest to the validity of the signatures.
Most other publicly traded financial instruments have similar protections. An exception would be bearer bonds. Bearer bonds are bonds for which ownership of the bond is not tracked, allowing the owner to remain anonymous. Stolen bearer bonds still wouldn't legally belong to the thief, but it would be much easier to get away with passing them off.