Here in Austin, that is fairly common. I store my rig well away from the city, although I do pay in price in gas and time to fetch and drop it off.
I've heard horror stories about some storage yards actually kicking and banning the victim off the property (making them take their rig off there and then or have the tow truck do it for them) if someone reports a theft. Yes, it is bad press, but when one person leaves, there is always another person willing to pay right behind them, and the theft issue is swept to the side.
As for trailer security, because they are so easily stolen, especially with a cordless angle grinder to tear off any wheel locks and such, a friend of mine secures his trailer in a way that has worked so far. He parks the trailer over a flush bracket in the floor, chains and padlocks the frame. Then, he hoists the frame with bottle jacks, sticks jackstands underneath, and then yanks the wheels off which get stored inside. So far, the worst that has happened is that people have cut the locks off the hitch and dragged his trailer half a block before realizing that it isn't going to go far, and the noise/sparks creates a spectacle.