RxJava - Using flatmap when return could be null

You should not return null but Observable.empty() instead.

.flatMap(new Func1<User, Observable<PutResult>>() {
    @Override
    public Observable<PutResult> call(User user) {
        if (user == null) return Observable.empty();

        //delete the session token and save
        user.removeSessionToken();
        return DatabaseModule.getStorIOSQLite()
                .put()
                .object(user)
                .prepare()
                .asRxObservable();
    }
});

It isn't clear what null you're talking about.

If you're asking whether the Observable<PutResult> can emit a PutResult that's null, then yes. This would result in a null being emitted by the outer observable.

If you're asking whether the Observable<PutResult> returned by the Func1 can be null, then no. Return Observable.empty() instead, (or Observable.just(null) or similar if you need to keep track of the number of emitted items).

In RxJava 2 null is considered to be an invalid value. You can use Maybe component in those cases , some thing like the below

  Maybe<Result>

   or 

  You can use flatMapMaybe<Result>