It seems that while you can't propagate incorrect unsigned transaction cause it won't be accepted to the pool you can still craft a block with bullshit and it's going to be processed just fine.

We should add a call to validate_unsigned in case we detect the extrinsic is unsigned transaction in apply_extrinsic and check that it returns TransactionValidity::Valid.

Alternatively the UnsignedValidator should have two different methods, where one is called during validate_transaction and second during apply_extrinsic phase. For convenience we can have a default implementation for the latter to just check for TransactionValidity::Valid.