Lawyers can't "hand over" your case, because unless you the client consents to their fee splitting, they don't get paid, and you have the absolute right to hire and fire the lqawyer of your choice. Each CA lawyer has to have a signed fee agreement with you, and if they don't, they're going to have a hard time collecting anything, especially if this is a contingency case.
So who's the last lawyer you actually retained? Ask them for an appointment to get a copy of your entire file so you can see what's been done, and get the current status. If necessary, you may have to report the last lawyer to the State Bar.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
Many attorney agreements allow an attorney to associate in other counsel and to have that other attorney do most if not all of the work. Check your retainer agreement and see if the attorney has that right. I don't feel you have a case for negligence until you've been damaged, and that means losing the case or missing a statute or losing some right on your behalf. That doesn't appear to have happened yet from the facts you've put in your question.
First you should talk to your current lawyer about the problems that you are having with him/her. If you are not satisfied, you always have the right to change lawyers. There is no case for negligence unless they have performed less than the standard of care and it has caused you damages. It is hard to tell from your question whether either of these conditions exist.
If your lawyer became ill and you agreed to a change of attorneys, your old lawyer may still be liable for negligent referral. however, who is to say that the case is down the tubes. If the case is still good, proceed with a new lawyer of YOUR choice and let the new attorney explore whether the old attorneys did anything wrong. Good luck, Claude
Sign up to receive a 3-part series of useful information and advice about personal injury law.