What will happen to Sirius B when Sirius A expands into a red giant?

In a billion years, when Sirius A expands and cools, will the nearby Sirius B be engulfed or will it have already faded away by then? Will B's orbit expand as the other star becomes larger? I think it would have enough gravity to not just be consumed, but I'm not sure. Thorough explanations would be amazing!