A business might pay an employee severance for morale purposes, good PR, and/or to entice the employee to sign agreements that reduce the business's future liabilities.
If an employee agrees to quit their job in exchange for severance money, this would result in lower unemployment insurance premiums (i.e. tax liability) for the business because the employee would not be eligible for unemployment benefits from the government. The more unemployment benefits former employees receive, the higher the unemployment insurance premiums for the business.