Depends on the airport. If it's a large international airport, with airliners parked overnight, then I'd expect that they would almost definately security onsite.
But many smaller airports doen't even have a fence around its boundary, and I certainly don't want to pay the increased landing/parking fees to fund it.
In either case, if my aircraft was damaged/stolen, I wouldn't expect the airport insurance to cover it, the same as if my car was damaged/stolen in a public car park.
Having said that I'd expect the airport to co-operate in finding the culpurit as much as possible, such as giving any CCTV footage that they have to the police etc.
It's not a nice thing to happen, and not a lot you can do about it either. I'm always very consious about the fuel when the aircraft is left at an unsecured airport. Not only what is taken out of the tanks, but also what could have been added to the tanks!