I was once part of a team that had a zero-storypoints developer too, let's call him Zero. He always refused to get any stories assigned during planning, his goal was always zero. He felt responsible for delivering all the planned stories and helped the people who struggled. He often came to me and told me to help someone on a specific task, because it was too much for him to help everyone.
This was well understood by management though. Zero took a 4-6 week vacation every year, and management always pushed important releases back if Zero was not there. The team could've done it without him, and it might've been better for the team not to have Zero around for all important releases. But management was scared something could go terribly wrong without him.