If you are already in them, then you do not lose access to them. To my knowledge you don't lose anything else, I've left plenty of Syndicates over the years (mostly as tests) but experienced no detrimental side-effects.
Kirsten is right, If you are an officer you can add or remove other officers. You can't remove a leader*. If you leave a syndicate, you will lose access to syndicate messages where bosses are posted. You may or may not annoy the syndicate members depending on who they are and how you leave. If you're in a syndicate with a lot of inactive members, you are better off leaving though. *Obviously as leader you can designate someone else to be a leader. A leader of a syndicate *must* do this before leaving a syndicate.
It's on server 2 where they dropped LCN-players when MySpace became DeathSpace. The problem is, there is a leader and only one officer. Both have not played for a very long time so I was wondering if they could be removed if I ask very nice to Mi7ch I know leaving is the only option at the moment but it would nice to rebuild the syndicate.