Airbyte's Schema Propagation feature helps manage unexpected schema changes in relational databases by allowing users to choose how they want to handle these changes. The DiscoverSchema process compares old and new schemas, detecting any changes at the source and automatically handling them based on connection settings. Users can configure connections with options such as propagating column changes only, propagating all changes, or ignoring and pausing the connection. This feature ensures there are no surprises in data when a change occurs, leading to fewer breaking changes, less worry about validating data, and stronger data contracts.