The bgsync _producer() method runs in a loop until stop() is called asynchronously.

If, after this critical section is run

https://github.com/mongodb/mongo/blob/ea1ad14260cad77823a549a22a32a97621d58a35/src/mongo/db/repl/bgsync.cpp#L425

stop() is called (as it would be during step-up), then before

https://github.com/mongodb/mongo/blob/ea1ad14260cad77823a549a22a32a97621d58a35/src/mongo/db/repl/bgsync.cpp#L441

is reached, the primary clears the applied-through time (as it normally does), the applied-through time will be re-set to the last applied optime. This state will persist until the next time the node becomes secondary and applies a batch. If the node restarts during that time, it will invariant and need to be re-synced.

We need to hold the mutex and ensure the producer is running while checking if applied-through is clear and setting it.