Replication Server records the DIST status of a distributor thread in the Replication Server rs_databases system table in the RSSD
A distributor (DIST) thread reads transactions from the inbound queue and writes replicated transactions into the outbound queue. A DIST thread is created when the Replication Server connects to the primary database, and can be suspended or resumed manually, or through a Replication Server configuration. Resuming and suspending a DIST thread modifies the DIST status of the thread.
The record in rs_databases allows the DIST thread to retain its status even after the Replication Server is shut down.
See Replication Server Reference Manual > Replication Server System Tables > rs_databases.