Data can be logged by Apple System Log (ASL) and remains on the log until the device is rebooted. Error logs are not bounded by the application sandbox.
This means error logs generated by one application can be read by other applications. Therefore, if applications log sensitive data, a malicious application can actively query for this data and send it to a remote server.
Error logs on the iPhone can be viewed by syncing the device with iTunes and looking at the Console app on OSX.