But on another side, if the company contacts the new company under no obligation, is this now retaliation against the employee for the losses the first company experienced?

This could become a sticky situation. The company has already experienced their loss and will hopefully take the measures to recover from the former employee. To take the step to jeopardize the employee from another job seems a bit much. How would they recover anything from the employee if they are not working at all.

Also, if the new company didn’t bother to check references or background checks they may not really even care if the former employer called at all.

I just think these are fine lines…..