They have a civil suit against him, but that kind of lawsuit is almost never successful (edit: at pinning liability onto the business owner - I'm saying liability will probably only fall to Twitter and not Musk personally /edit). Twitter is still a limited liability company, and now that it is privately owned its owners are free to run it into the ground - they don't have an obligation to shareholders.
Private businesses should be free to do this, but this was a publicly traded company turned private, so arguably there should be solid protections in law that make this wrong rather than the only option being a difficult civil lawsuit.