Since the stars have aligned right, I was able to make a little test: I've left insufficient funds on my card so the monthly fee made it get negative.
I don't know if it's a new feature or not, but I've got this morning a push notification telling that I am on negative balance. No extra explanations, but it's still something.
Of course, they could have sent an e-mail since push notifications are easy to miss (for example by disabling them after they've started spamming offers). However, a little warning is there.

I know the case is closed, but I thought I should add this in case somebody else will read about the negative funds issue.