An MPL holder is tied to the company they are flying with until reaching 1500hrs when it can be exchanged into an ATPL. If one fails to reach 1500hrs in that company, under special approval the person could work in another company, however I find it very unlikely that some other airline would go through all this approval process just for you. Another, more realistic option is crediting the hours towards a modular CPL course...
In my point of view, there is no better way for a pilot to train from zero to a copilot, than MPL with only let's say 240 hours. So much multi-engine multi-pilot experience and even the base training is doubled, the pilot should feel like a fish in the sea when stepping on board the aircraft for the first flight of line training. BUT the gods of aviation decided to make it that much complicated for guys who (might) fired from their jobs.. However job guarantee? mmm, tempting