At the end of the second season the dog will die defending Picard. Patrick Stewart will have a brief scene mourning the dog to show off his acting chops, and then the dog will be brought back as a synth, along with an explanation that nothing has really changed for the dog. Picard will buy a convertible Corvette, and together he and the dog will travel the US looking for interesting characters to interact with (think a small community of Amish-like Borg) and wrongs to right.