Although Im no security expert, Ive been told by a shop that it is possible to bypass the immobilizer using a bypass kit. They hinted at another way of saving money and not buying the bypass kit by disabling the immobilizer altogether. If this was the case, they would get away with using a nonchipped key. Im not saying it was the shop, but if they drove it away, thats how I think they did it.
What I dont understand is why somone would steal a corolla. This is not a fast car, and there is virtually no market for oem parts(chop shops). I hope they recover it, but at the worse somone will be driving it around for a year.