S.D. Codified Laws § 60-4-3

An employee, unless the term of the employee's service has expired, or unless the employee has a right to discontinue it at any time without notice, shall continue service after notice of the death or incapacity of the employer so far as is necessary to protect from serious injury the interests of the employer's successor in interest, until a reasonable time after notice of the facts has been communicated to the successor. The successor shall compensate the employee for the service according to the terms of the contract of employment.