The program will now pay for reports of third-party services that might expose the bits of information that Facebook uses to identify you. That information is known as user tokens.
Only apps that allow give you the option to "log in with Facebook" are affected by the changes announced Monday.
The new program covers apps and websites that are leaking user information through cybersecurity flaws rather than by selling them.
"If exposed, a token can potentially be misused," said Dan Gurfinkel, security engineering manager at Facebook, in a blog post published Monday. "We want researchers to have a clear channel to report these important issues, and we want to do our part to protect people's information, even if the source of a bug is not in our direct control."
Facebook new bug bounty program will pay at least $500 per app or website found to be exposing user tokens.
The program is another way that Facebook is attempting to show users it's trying to keep their data safe after the Cambridge Analytica privacy scandal enveloped the company in March.
The company created a separate bug bounty in April that offers rewards for finding third-party services that are abusing Facebook user data.