Are AI chatbots capable of remembering the information you provide to them?

A user on Reddit inquired whether AI chatbots like ChatGPT or Claude retain information provided by users. The user, an amateur writer, is concerned that if they submit story ideas or excerpts for feedback, the chatbot might store this information. Consequently, a different user asking for a similar idea could potentially receive the original user's submitted content, raising questions about data privacy and intellectual property within AI interactions.