In the Tudors it is suggested to Catherine of Aragon to join the nunnery so that she can “choose” to annul the marriage for the Church. Why did Anne not choose this as a way to avoid execution?
Although Sir William Kingston reported "Yet this day at dinner the Queen said she would go to “anonre” [a nunnery], and is in hope of life", which suggests that Anne was offered such a deal by Cranmer when he visited her in the Tower on the 16th May 1536. However, if it was mentuoned to her, it was never a serious deal. Henry VIII had already ordered the French swordsman from Calais, Anne had already been tried, found guilty and condemned to death, so I think that Cromwell and/or the King were just trying to get Anne to agree to the annulment and bastardisation of Elizabeth, by giving her some hope. Henry needed rid of Anne and he needed her to go permanently, she had to die. It would have been too much of a risk to leave her alive.