The place to start is your LLC operating agreement. Does it contain any restrictions upon the sale or transfer of LLC interests by members? If not (or you don't have an LLC operating agreement), then your LLC is covered by the default provisions of the Delaware LLC Act. In particular, § 18-702 has bearing on this issue. It provides, in pertinent part:
§ 18-702. Assignment of limited liability company interest.My reading of the above language is that the other members may sell their LLC interests; however, the purchaser does not become a member of the LLC unless the remaining LLC members vote unanimously to admit the purchaser as a member. What does the purchaser get if is blocked from becoming a member? The right to share in the LLC profits and losses and to receive any distributions otherwise allocated to the LLC interest purchased. Can the purchaser vote you out as managing member? I don't see how that happens without your consent to make the purchaser a member. Unless important facts are missing from your question, this transaction is highly unlikely to happen without your consent.
(a) A limited liability company interest is assignable in whole or in part except as provided in a limited liability company agreement. The assignee of a member's limited liability company interest shall have no right to participate in the management of the business and affairs of a limited liability company except as provided in a limited liability company agreement and upon:
(1) The approval of all of the members of the limited liability company other than the member assigning the limited liability company interest; or
(2) Compliance with any procedure provided for in the limited liability company agreement.
(b) Unless otherwise provided in a limited liability company agreement:
(1) An assignment of a limited liability company interest does not entitle the assignee to become or to exercise any rights or powers of a member;
(2) An assignment of a limited liability company interest entitles the assignee to share in such profits and losses, to receive such distribution or distributions, and to receive such allocation of income, gain, loss, deduction, or credit or similar item to which the assignor was entitled, to the extent assigned;* * *
What about the loan used to purchase the business? The selling members are not relieved or any LLC debt they guaranteed merely by selling their LLC interest. Any deal to replace the purchaser as guarantor on this debt for the sellers is matter to be negotiated privately with the lender. It may be that the sales price is assumption of the debt.
As always, the best advice is to address restrictions on transfer of LLC interests in the LLC Operating Agreement at the initial formation of the LLC.