Correct, the workflow's guarantee to always complete executing independent of process/hardware failures is dependent on the database not losing data. You host your workflow code with Temporal's Worker library, which talks to an instance of the Temporal Server [1], which is an open-source set of services (hosted by you or by Temporal Cloud), backed by Cassandra, MySQL, or Postgres. [2] So for instance increasing Cassandra's replication factor increases your resilience to disk failure.
[1] https://github.com/temporalio/temporal
[2] https://docs.temporal.io/clusters#persistence