When content is removed after a DMCA notice, the person who uploaded it can file a counter-notice stating, under penalty of perjury, that the material was removed by mistake or misidentification. The counter-notice must include their name, address, and consent to the jurisdiction of a federal court.
After receiving a valid counter-notice, the service provider forwards it to the person who filed the original notice. The provider can then restore the content no sooner than 10 and no later than 14 business days later, unless the copyright owner notifies them that a lawsuit has been filed.
For creators, counter-notices against leaked content are uncommon, partly because the person filing has to identify themselves and accept a court's jurisdiction. If you do receive one, keep your records, consider whether the content is worth defending, and talk to a lawyer. Privly tracks counter-notices on notices it files and will let you know if one arrives.