It becomes a negative avios balance with the credit card provider (usually Amex, as in your case), but it will not be taken from your BA account.
If you then close the credit card whilst in a negative balance you may be in breach of the terms with Amex but I doubt they would take any action, particularly when it isn't done deliberately.
Also a similar thing can happen if the purchase triggers a voucher but is then refunded.
As I say, I am sure in the majority of cases these are innocent but I am also sure that Amex would be able to work it out pretty quickly if it became a pattern.

I recently had a large refund to my BA business Amex after I eventually took delivery of an electric car I have been on a waiting list for a long time for and they refunded the deposit....!
I am still in negative balance and will be for some time as almost all of my business CC spend is now on an Amex Platinum.