I don't think it's true to say that they are desperate for a job working in a house for very little money.

Given how many hundreds and hundreds runaway after arriving, many of them just accept the job because it gets them an entry visa into Qatar, and they know they can make 10 times as much working as a casual maid cleaning the houses of a bunch of westerners, than they will working for a single family.

It then becomes the embassy's problem to try and clean up the mess when they get caught and deported.