When a partnership terminates, the business of the partnership ends except for purposes of liquidation.
If a partnership terminates because its membership is reduced to one person, that person is not bound to liquidate the partnership and may continue the business as a sole proprietor. If the person elects to continue the business, his former partners are entitled to amounts equal to the value of their shares as of time the partnership terminated, and they have the right to demand security for the payment of partnership debts.
La. C.C. § 2828