dying dog long please help

My boyfriend of 4 years has a dog who is around 15 or 16 and is dying, the dog will not eat or sleep and can hardly walk. The dog has lost a major amount of weight and has a lump in his throat, when have been syringe feeding the dog for about a month now and nothing is helping. The dog has never been to the vet because he is a runt and an inbread mut. When the dog was a puppy, all of the other puppies in his litter had their shots and died so they never gave this dog shots and he has lived a long full life. It has come to the point where there is talk about putting my boyfriends dog to sleep and letting him go now before he gets any worse or hurts any worse. I love this dog as my own since he has been part of my life for 4 years and it is hard on me but it is even harder on my boyfriend who has lost 3/4 of his grandparents within the past 5 or so years and is now losing his dog that he has had for 15-16 years. What do I say what do I do and how can I help make this any easier.