Monzo doesn’t charge any fees so you wouldn’t go into an overdraft. It’s almost impossible to go into an overdraft with your prepaid card. If you did manage to, there still aren’t any charges for this listed in the T’s & C’s.
As far as I know, your account would remain open, although once Monzo launches it’s current accounts (& issues new debit cards) I expect the prepaid cards will be deactivated at some point. Obviously Monzo would give you notice.
Yes…you really won’t want to cancel it though! https://twitter.com/MonzoLoveTweets 