This question is stressful to most attorneys. If a malpractice judgement is entered against an attorney who does not have malpractice coverage , the attorney is personally liable and the party can levy against certain assets of the attorney.
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What Ms. Goldstein is correct, and the attorney will also have to hire his own attorney. Usually malpractice insurance companies, like most insurance carriers, have a "duty to defend" and usually provide attorneys (often "captive attorneys" who are employees of the insurance company with a law firm like sounding name).
That being said, an attorney without malpractice insurance may also have very few assets, and thus be relatively judgment proof, just like any judgment debtor with few assets. Malpractice insurance also usually has a deductible, and often settlements for weak or nuisance cases, will often just be twice the deductible, with the insurance company and the attorney sharing the pain.
As I've said in answers to questions generally about malpractice, it must be a very clear instance of the attorney dropping the ball and committing gross negligence, such as missing filing "drop dead" filing deadlines or misappropriating escrow funds, and you must show that the attorney's negligence exclusively caused your loss.
Bad advice or tactics or misunderstandings of the law or losing a case are generally not malpractice, unless everything entirely hinges on the attorney's acts and omissions (as it seldom does in real life, the attorney doesn't make the facts and you can generally point to at least several reasons for losing a case that aren't related to the attorney's errors).
And unlike most personal injury cases, it is difficult for the plaintiff to get another attorney to take the case on a contingency basis, and unless there's bad faith or wrongdoing on the attorney's part, or some statutory basis, the plaintiff will have to pay for his own legal fees.
I'd therefore say, all things considered, that a plaintiff in most cases other than those with clear cut attorney error (like missing a statute of limitation), you'd be less likely to receive a settlement if an attorney does not have malpractice insurance. (But I'm kind of speculating here, but insurance companies, like municipalities, don't like to settle on anything but a "nuisance suit" minimal settlement basis for anything but the most clear cut instances of potential malpractice verdicts).
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The attorney will have to defend themselves and/or pay out of their/their firm's "pocket" to hire defense counsel. Any settlement/verdict would be paid by the attorney/firm's "personal" assets. Joint assets held with a spouse, etc. will likely not be available to satisfy any settlement/verdict absent some type of fraudulent transfer. Collectability could become a problem for you if there are not sufficient personal/firm assets (and you should sue the attorney and the firm the attorney works at, to broaden your range of potential assets available to satisfy and settlement/judgment).