While shadow Redundancy is the mechanism used to provide high availability for messages in transit and the DAG is the primary mechanism for mailbox high availability, safety net (formerly known as the transport dumpster) is designed to keep a copy of messages that were processed successfully by a server for a configurable amount of time.
First released in Exchange 2007, the "transport dumpster" underwent some significant changes in Exchange 2010. These changes allowed the transport dumpster to help protecting database copies in a DAG by keeping messages that weren't replayed into passive database copies yet. Although its purpose hasn't changed much in Exchange 2013 "safety net", has been improved greatly yet again.