Your answers to questions, quizzes, and other conversation types won't be lost if you cancel your subscription. Your memories, added to the Timeline, will also remain—the progress with your partner is not attached to any membership.
However, when using the free version of Paired, you'll only have access to some parts of the app:
the Conversation of the day (either a question or a quiz)
the Timeline
other Special Dates and reminders
If you have any more questions on this topic, please let us know with a description of the problem and a screenshot of any error message you see. We'll make sure to investigate further!