I’ve been told that a woman who was married, had children, and then got an annulment became a nun later in life. Is this possible?

Yes. And the same thing can happen with men becoming monks. It also sometimes happens that a religious order will accept an individual who is widowed rather than divorced. Such cases tend to happen only after the children are grown, since there is a grave moral obligation for parents to see to the support and education of their children. This makes such cases uncommon, since religious orders normally do not accept new members who are above a certain age. However, it is possible.