I don't understand why you would go to the expense of a microchip and then not register it
There are a myriad of reasons one might not register the chip after paying for the dog to be chipped. One might be laziness or forgetfulness, another might be financial not knowing there is an additional cost for registration as well as periodic renewals. It also seems common that the vet or their staff does a poor job of explaining to the owner that the chip needs to be registered. That is an issue according to my former vet and one of the reasons my current vet includes the initial registration in the chipping price. He or one of his staff has the owner fill out the paper work prior to doing the chipping. That way the price, and need to register is taken care of and the added cost of renewing is learned.
As mentioned, the owners can still be tracked down even if the chip is not registered. It does taken more effort and time but it is considerably less than posting signs and calling local breeders, shelters, and pounds.
Last but not least, good job taking in this dog and the effort put in to find the owner. It is sad the original owner thinks so little of the dog but it was to your benefit. You will have your work cut out as the dog has learned to find freedom by digging under obstacles. That is a habit that probably won't be broken. I learned to sink hog panels under the kennel to stop the digger I had, that is until I replaced the gravel with cement. I also had to put a cover over the top of the kennel as that dog learned to climb the chain link fencing as it preferred to be running free.
Again, good for you for caring enough to help this dog out. Sounds like it really needs it.