That use to happen to me a lot when I had my Jeep Wrangler. But I was lucky because its kinda made for that. So it caused no problems

 

My MINI is a tintop, but I often leave the top on our Jag (a '96 XJS) down when I park just about anywhere it's not supposed to rain. In fact it pretty much just doesn't get driven if it's going to rain and the top stays down 80% of the time. It does have an alarm that goes off if you reach in, but no one has tried yet - I'm the only one who sets the stupid thing off when I forget that it's locked.

 

I leave mine open from now until November (only comes up for rainy days) -- a risk I'm willing to take.

By the way, another thing that can be easily stolen with top down is whatever CD is in your head unit. It can be ejected without the keys/power.... and I guess someone could sit in the cabrio and listen to the radio.