I am sure that there will be many opinions. The way I see it, Candy feared two things in equal proportion.
First, he feared dying alone. Candy in the book is an old man. The best years of his life are now gone. The book does not say it, but we can assume that many people in his life have passed away. This means he is more and more alone. This is why he is so attracted to his dog and feels the attraction of the friendship of George and Lennie. He wants to be a part of their dream and life. In this way, he won't be alone.
Second, Candy also feared being expendable. In a very touching scene, the men tell Candy that he should get rid of his dog. Candy objects. His dog has been with him all of these year. How can he get rid of him now? The men give their arguments. The dog is old, good for nothing, and won't even feel pain when they shoot him. Symbolically this is Candy. He is handicapped and old. Do people really need him?