I'm just glad that she had the roof down in the first place ! Britain has more convertibles than sunny countries like Italy, despite our awful weather, and all you normally see, even on a lovely day, is people driving around with the roof UP !
I have left mine locked with the roof down if I'm popping into a shop. I don't leave anything in view that can be pinched and the car is alarmed and imobilised.
Very rare that I leave mine parked with the roof down but if I do I always make sure it's locked ( even in my garage ), because has emeritus say's it also activates the engine immobiliser.
Mine had a sensor that would activate the alarm even if someone leaned into the car. Gave my boss a fright when he leant in to pick up a coat I'd left on the passenger seat.