User embeddings play a crucial role in user engagement forecasting and personalized services. Recent advances in sequence modeling have sparked interest in learning user embeddings from behavioral data. Yet behavior-based user embedding learning faces the unique challenge of dynamic user modeling. As users continuously interact with the apps, user embeddings should be periodically updated to account for users' recent and long-term behavior patterns. Existing methods highly rely on stateless sequence models that lack memory of historical behavior. They have to either discard historical data and use only the most recent data or reprocess the old and new data jointly. Both cases incur substantial computational overhead. To address this limitation, we introduce User Stateful Embedding (USE). USE generates user embeddings and reflects users' evolving behaviors without the need for exhaustive reprocessing by storing previous model states and revisiting them in the future. Furthermore, we introduce a novel training objective named future W-behavior prediction to transcend the limitations of next-token prediction by forecasting a broader horizon of upcoming user behaviors. By combining it with the Same User Prediction, a contrastive learning-based objective that predicts whether different segments of behavior sequences belong to the same user, we further improve the embeddings' distinctiveness and representativeness. We conducted experiments on 8 downstream tasks using Snapchat users' behavioral logs in both static (i.e., fixed user behavior sequences) and dynamic (i.e., periodically updated user behavior sequences) settings. We demonstrate USE's superior performance over established baselines. The results underscore USE's effectiveness and efficiency in integrating historical and recent user behavior sequences into user embeddings in dynamic user modeling.