can cat-hating dog be rehabilitated?

Question
QUESTION: We had a 12-year-old cat and a 13-year-old labrador when we adopted a 1-year-old rescue dog (mostly labrador, we think). The dog and cat got off to a bad start, with the dog chasing the cat the first day. We worked with both pets and in time we worked out a system that seemed to work. The cat stayed in the basement most of the time, except when the dog was sleeping in our room. When they would meet by chance, they'd stare daggers at each other, but the dog did not attack. I usually ended the encounter by taking the cat downstairs. This is how it has been for 2 years.
The other day, the cat got out into the backyard at night and we did not know it. When I woke at 5 in the morning, I took the dog for a short walk, then put him in the backyard for his breakfast, as I usually do.
We found the cat dead in the yard about an hour later. We did not hear a fight, but our windows were closed. Could the dog have not recognized the cat in the dark? Or did he think the rules of the house didn't apply outside?
Can he be rehabilitated at all? He's a sweet and gentle dog with humans. He has a bit of fear-agression with some other dogs, but that has been improving a lot in the past few months. He's even made a few friends among other dogs in the neighborhood.

ANSWER: A dog that has not been habituated to, and socialized with, cats in the first few months of life will have a strong drive to chase (and often kill) the cat, seeing it as prey.  There were no "rules" in your house, other than your cat having been banished to solitary confinement in the basement for two years.  You did absolutely nothing to solve this problem except make that cat's life miserable and allow its life to end in an excruciatingly terrifying manner.

---------- FOLLOW-UP ----------

QUESTION: It really doesn't help me, my dog or even my cat to pile guilt on me. I followed many experts advice to try to help the two animals accept each other: I exposed the cat and dog to each other's scents, sat with my cat on my lap with my dog in a crate. I spent lots of time on this. I'm sorry it didn't work, and I already am devastated by the loss of my cat. I was seeking help and advice, not judgement. I'm sorry I bothered you.

Answer
No doubt the experts' advice was given over the internet.  NO experienced behavior expert, paid to come into your home, would ever have suggested what you described.  The humane society should have been called to your home to rescue that poor cat, isolated and neglected in the basement.  You were totally remiss in your responsibility toward both these animals.  The guilt is clearly yours.