I have read the manga and I know that the Baskervilles are the supporters of Glen Baskerville, but what is their real job? Is it to protect the abyss or to make the abyss come to the earth and destroy it so they can find the core of the abyss?
The Baskervilles hold chains and one of the doors to the Abyss. According to the Pandora Hearts wikia:
It is implied that the Abyss surrounds the world, as if the chains holding the world together are destroyed, the world will fall into the Abyss.
Chains can leave the Abyss by contracting with humans and Baskervilles
[Levi] continued to explain that among the Baskervilles' many duties to maintain a harmony within the Abyss, was protecting the Chains to prevent their destruction.