I assume you want to clear the BehaviorSubject (because otherwise don’t call onComplete on it). That is not supported but you can achieve a similar effect by having a current value that is ignored by consumers:
public static final Object EMPTY = new Object();
BehaviorSubject<Object> subject = BehaviorSubject.createDefault(EMPTY);
Observable<YourType> obs = subject.filter(v -> v != EMPTY).cast(YourType.class);
obs.subscribe(System.out::println);
// send normal data
subject.onNext(1);
subject.onNext(2);
// clear the subject
subject.onNext(EMPTY);
// this should not print anything
obs.subscribe(System.out::println);