Unlike medical insurance for Americans, though, pet insurance does not cover preexisting conditions. That means, if your dog is ill with a certain condition before enrollment, the insurance company will not cover the expenses spent for treating that illness. Actually, most pet insurance firms will not cover that specific condition even after your pet is treated. There are, though, a few exceptions, that make the difference between curable and incurable preexisting conditions, allowing you to insure your dog for that condition if it is cured, after a certain time frame.