emirates – Do airlines compensate passengers if they allow them to board with an invalid Visa card?

No, it's the opposite.

It is always the responsibility of the passenger to ensure that he has all the required documents (passport, visa, etc., with the appropriate validities, etc.).

Airlines do not check these documents before boarding for passenger comfort, but because the country of destination requires it, directly or indirectly: it turns out that the passenger is not eligible to enter for lack of proper documentation, this is usually the case. airline is required to return them at their expense, and they may also be fined.

The transportation conditions of most airlines are very explicit about this and may even indicate that they may charge you fines / penalties because of you.