What kind of contract at what kind of agency?

Did client work there?

Why does client say it is nonbusiness?

The spouse bought out the husbands contract for an agency for not completing his contract for work

So basically it was a breach of an a employment agreement

If someone said it is deductible, where would you propose to deduct it?

Employee signed a contract to stay for a year.  Employment agency got paid a percentage of his salary for a year.  He left early.  Agency lost money.  He paid them the difference.  See explanation and example below.  (The employer might have paid the fee while he was working, or he might have been paying it himself from each paycheck.)  These used to be deductible as a miscellaneous on Schedule A, but not since 2017.  

Applicant-Paid Fees

With this arrangement—also referred to as the employee-paid fee—the employment agency fees are charged to the applicant for the service of finding an employer. This normally entails an employment agency, which acts as a staffing agency, claiming a portion of a worker's hourly pay during the term of a contract.

For example, if a worker is offered a 12-month contract position at $49 an hour, the hiring company may have actually budgeted $60 an hour. The employment agency may pocket the difference or a portion of the difference in lieu of a one-time fee without the employee ever knowing of the arrangement.

https://www.investopedia.com/terms/e/employment-agency-fees.asp# 

A client was in a 3 year contract with an employment agency as a nurse, within a year he decided to buy out the rest of his contract of $30,000. During the time as a nurse he had a 2nd job working from home as a patient screener and received a 1099nec of $50,000. Client claims that he used $30,000 from his patient screener job to pay off the agency contract. So now the question is, can we claim the $30,000 agency buyout as an expense on the Schedule C?

Funny how the facts change. First he paid it. Then his wife did. Now it's "related" to his 1099-NEC income.