Anyone who has suffered damage as a result of infringement of GDPR has a right to receive compensation from the controller or processor.
This means that if you are a data controller who uses a 3rd party processor which suffers a breach, you could potentially be sued for the damages caused. If you are a data processor however, you are only liable for your own infringement of GDPR.
If multiple data controllers or processors are involved in an infringement, any liable party can be sued for the full amount of damages. However once they have paid the damages they will have the right to claim compensation from the other parties involved.
Article 82 text:
1.Any person who has suffered material or non-material damage as a result of an infringement of this Regulation shall have the right to receive compensation from the controller or processor for the damage suffered.
2.Any controller involved in processing shall be liable for the damage caused by processing which infringes this Regulation. A processor shall be liable for the damage caused by processing only where it has not complied with obligations of this Regulation specifically directed to processors or where it has acted outside or contrary to lawful instructions of the controller.
3.A controller or processor shall be exempt from liability under paragraph 2 if it proves that it is not in any way responsible for the event giving rise to the damage.
4.Where more than one controller or processor, or both a controller and a processor, are involved in the same processing and where they are, under paragraphs 2 and 3, responsible for any damage caused by processing, each controller or processor shall be held liable for the entire damage in order to ensure effective compensation of the data subject.
5.Where a controller or processor has, in accordance with paragraph 4, paid full compensation for the damage suffered, that controller or processor shall be entitled to claim back from the other controllers or processors involved in the same processing that part of the compensation corresponding to their part of responsibility for the damage, in accordance with the conditions set out in paragraph 2.