Airbyte continues to sync data using the configured schema until that schema is updated. Because Airbyte treats all fields as optional, if a field is renamed or deleted in the source, that field simply will no longer be replicated, but all remaining fields will. The same is true for streams as well.
For now, the schema can only be updated manually in the UI (by clicking “Update Schema” in the settings page for the connection). When a schema is updated Airbyte will re-sync all data for that source using the new schema.