Data Care Act of 2019 This bill imposes various duties on online service providers with respect to their handling of individual-identifying data that can be reasonably linked to a specific user. Specifically, online service providers have a duty to (1) reasonably secure such data from unauthorized access, (2) refrain from using such data in a way that will result in reasonably foreseeable harm to the end user, and (3) not disclose such data to another party unless that party is also bound by the duties established in this bill. The bill authorizes the Federal Trade Commission and specified state officials to take enforcement actions with respect to breaches of such duties.