Saleen chucked the Eternal Control Shard into the figure's head and Baudelaire's soul entered it. No one truly wanted to die, especially someone like Baudelaire. He had an intense hatred for the Holy See and, given how Saleen had given him a chance, he had to continue living.
After all, he had only sold his soul to the God of Purgatory to exact his revenge on them.
It was all the same to him regardless of who he swore his allegiance to, so long as the one he served was against the Holy See. Baudelaire's soul had already been twisted and he had no other desires. His only meaning in life was to go against the Lord of Glory.