To protect users' right to be forgotten in federated learning, federated unlearning aims at eliminating the impact of leaving users' data on the global learned model. The current research in federated unlearning mainly concentrated on developing effective and efficient unlearning techniques. However, the issue of incentivizing valuable users to remain engaged and preventing their data from being unlearned is still under-explored, yet important to the unlearned model performance. This paper focuses on the incentive issue and develops an incentive mechanism for federated learning and unlearning. We first characterize the leaving users' impact on the global model accuracy and the required communication rounds for unlearning. Building on these results, we propose a four-stage game to capture the interaction and information updates during the learning and unlearning process. A key contribution is to summarize users' multi-dimensional private information into one-dimensional metrics to guide the incentive design. We show that users who incur high costs and experience significant training losses are more likely to discontinue their engagement through federated unlearning. The server tends to retain users who make substantial contributions to the model but has a trade-off on users' training losses, as large training losses of retained users increase privacy costs but decrease unlearning costs. The numerical results demonstrate the necessity of unlearning incentives for retaining valuable leaving users, and also show that our proposed mechanisms decrease the server's cost by up to 53.91% compared to state-of-the-art benchmarks.