Existing bearer bonds and shares are not illegal but it is no longer legal to issue new bearer shares and bonds in virtually all countries. Maybe somolia allows it but even many offshore locations revised their statutes in the last couple decades. There are a lot of outstanding US treasury bearer bonds. They no longer pay interest but they are normally used as a "reallllly" big cash note so they probably will never be redeemed.
BTW: Nevada prohibited the issuance of bearer shares in 2007.
http://law.justia.com/codes/nevada/2010/title7/chapter78/nrs78-235.htmledit: is it possible to create a blockchain based registry of ownership and not have them be bearer shares?
Sure if the blockchain can verify the identity of all shareholders, collect and store required information, ensure shareholders are accredited before issuing shares, enforce restrictions on transfers for private placements as required by securities laws, and file all necessary documents with regulators in a timely manner.