Buy Out contract of an agency

What kind of contract at what kind of agency?

Did client work there?

Why does client say it is nonbusiness?

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#