Yes they can! but never cooked bones! The Yorkie Forum
Contrary to popular belief, even very small yorkies are able to chew and even consume bones, though it is obviously a bit more of a challenge and it is something they must learn if not accustomed to.
Yorkshire Terriers are dogs, although bred with beautiful long hair, charming little characters and often only kept indoors, they are still dogs and all dogs need to chew and even consume bones.
This instinct is so strong that they start to chew everything from when they puppies. Giving your Yorkie bones will also make it easier to stop him chewing on the furniture!
Is it dangerous?
It can be. NEVER FEED COOKED CHICKEN BONES TO YOUR DOG! Though raw chicken bones are most suitable for yorkies.
Cooked bones are very dangerous, they often become brittle and have less nutritional value.
When a dog is not accustomed to receiving any particular food, it is best to supervise him in the beginning until you are confident he has learned to eat it properly.
A chicken neck is good, with good bones that any size yorkie can chew, but a Yorkie puppy can choke on it.
Supervision is necessary in the beginning.
Why is it important?
Other than the obvious reason to clean their teeth and to give them strong healthy jaws and gums, raw bones are very nutritious. The marrow of the bone is especially good for them in a number of ways including a healthy coat. The calcium from the raw bone is more digestible and the larger pieces stay in the stomach longer allowing digestion to take place and absorption of all those necessary minerals.
Most important, dogs love bones and it makes them happy to chew on them. According to the book "Your Adopted Dog," when dogs chew, endorphins are released from the brain. These chemicals are thought to make dogs feel good.
Why won't my Yorkie eat bones?
If your Yorkie has grown up from puppy-hood without bones, he will have weaker jaws and will be unable to crush them. Start giving him softer small bones like chicken( even a chicken head with the beak clipped off), with a little raw meat on, he will eat it. Keep giving softer bones until his jaws have strengthened and then give some mutton bones or pork, beef has very hard bones and they will tend to bury them.
Keep trying different bones until you find what suits your yorkie best. He will be very happy.
Do not be surprised when your tiny Yorkie, eventually after some months of practicing, starts devouring even large bones with relative ease, this is good!