It depends. Your separated employees can continue to repay their loans in substantially equal installments, if the plan allows it. Check your plan documents, and check with your plan administrator. You also would have to determine how problematic it would be, from an administrative angle, to succeed with that repayment strategy since payroll deduction (the method used with employees) would no longer be possible.
Also, while the law does not prohibit continuing repayment after termination of employment, it is clear that once the "contract" has been violated (i.e., the repayment schedule is no longer met by a former employee), there is a deemed distribution. Making sure the payments are made on time and in equal installments is a challenge that many administrators do not want to tackle.
Because a loan in default is considered to be a plan asset, interest on it continues to accrue even if the loan is treated as a deemed distribution. However, that accrued interest is not included in a 401(k) participant's income.
Source: IRS Reg. §1.72(p)-1, Q&A-19(a)