Nice to hear what woodside farm says and yes I will always agree its how you bring them up, but unsupervised it can sadly be a very different story.
Dogs are by nature territorial - terriers in particular (not sure if thats where the name came from). If a fox had tried to come in whilst the dog was there, I'd be very surprised if a challenge hadn't been made by the Jack who (quite rightly) thinks its his patch.
Nobody knows if the chickens hadn't been inadvertently "winding" the Jack up ever since he was first introduced.
Dogs invariably will operate and exist within a pecking order. You, their owner, or another human with enough command, will always be top dog in the order (unless anothe wild animal can top that). The dog may feel he's bigger than he is, but whilst you are there he will generally, toe the line. Given his freedom , without you there, he's got the run of the place - he is top dog. That, in some breeds can bring out the "control freak" if you will, and the killer instinct kicks in. He's asserrting his perceived place at the top of the pecking (and food) order.
Sorry if this sounds brutal, but it is the generally held "law of the jungle".
The only other senario, I can come up with is, if the fox did get in and do the deed, the dog would be automatically drawn to the smell of blood, and probably want to taste the blood - they are happy to eat raw meat after all, so not surprising that blood is found round its mouth.
If the Jack hadn't had it's dinner already that morning and was hungry, all the more reason for his feasting - whatever the catalyst
Don't know if you saw this news article a few weeks back
http://www.express.co.uk/features/view/93772/Castaway-dog-survived-months-on-desert-isleIt was the best I could find on google front page, but the previously domesticated dog reverted to natural instincts for food. Winding up is the other senario.
Pass my sympathies on to your Mum - not good to lose any animal