Your question is confusing. I agree with Mr. Brinkmeier that each side has to pay its own legal fees, but sometimes if the lawyer on the other side did something that caused the opposite party additional legal fees to address, like frivolous litigation or claims barred by a statute of limitations, it's possible for the other side to recoup attorneys fees from the other side caused by such shenanigans. Is this what you're trying to suggest. I'm not able to totally decode your question.
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The answer is no. Each side pays for their own lawyers fees. If you were to lose the claim and a jury found there was no malpractice you will not have to pay the other sides legal fees either.