As reported in an article in The Business Lawyer:
In Anthony v. Blum,(1999 WL 259726 (Conn. Super. Ct. Apr. 23, 1999)). a Connecticut case, Blum had negligently represented Anthony and, in settlement, Blum executed a $10,400 promissory note on behalf of his law firm (an LLC), payable to plaintiff. Plaintiff sued Blum on the note and argued that Blum's negligence constituted the consideration for the note, thereby entitling plaintiff to hold Blum personally liable. The court held, however, that "the present action is not a malpractice action but a breach of contract action" in which the law firm was the obligor and for which "Blum is not personally liable."
So, the lawyer escapes liability on the note issued by the LLC to settle the case based on the lawyer's malpractice. No wonder lawyers have a bad reputation for slick maneuvering.