The three partners presumably created some variation of an § 705 BGB partnership (Gesellschaft bürgerlichen Rechts). Their rights and obligations are established via their mutual contract, which does not even have to be written as long as no real estate is involved. However, this contract is bounded by the BGB.
The partner A who wants to leave can terminate the partnership contract at any time. Depending on the terms of the contract, this will dissolve the partnership (default consequence), or the partnership will continue with the other members B and C. In either case, A will receive their share of the assets of the partnership. The BGB provides a default procedure:
- objects that were handed over to the partnership are returned, without compensation for use or accidental loss
- outstanding debts of the partnership are discharged, or sufficient assets are set aside for later discharge
- from the remaining assets, A's capital contributions are returned. This includes both monetary and non-monetary contributions, but not services performed by A.
- if there is a surplus/profit, it is divided among the members. However, the correct division can be difficult to determine since it shall depend on the member's share/contribution to the profit, not necessarily on their capital contributions to the partnership.
- similarly, if there is a deficit, everyone has to make further contributions to the degree that they are responsible for those losses
So this means that yes, for all practical purposes the partners B and C can “buy out” A, if A voluntarily terminates the contract. B and C would have to pay to A either according to the terms set out in the contract, or by default:
- A's capital contributions to the partnership
- plus/minus the profit/losses for which A is responsible
Since you mention that the founder's agreement describes an allocation of “equity”, this may help with the division of profits.
But starting with a non-notarized partnership and presumably shoddy bookkeeping, trying to reconstruct all contributions and everyone's share of the profit/losses is going to be an utter mess – the typical divorce is probably easier to sort out. If there are non-negligible sums involved, everyone (and especially A) should get a lawyer to represent them in the ensuing negotiations. Nothing prevents the partners from reaching an unanimous agreement, but everyone would still be interested in getting this agreement negotiated by legal professionals to make sure that no future demands remain. Legal professionals are costly, but if this startup idea works out these DIY contracts will end up being far more costly.
Further potential factors that might complicate things:
- depending on the goals or the structure of the partnership, different rules might apply. In particular, this might be the case if the goal of the partnership was trade.
- Some of the non-monetary assets that would return to A might be essential for the continuation of the partnership by B and C. This would give A substantial leverage during negotiations, unless there are already contractual provisions for continued use. For example, the comments point out issues around intellectual property.
- A is not required to exit the partnership. B and C can exclude A from the partnership only with cause, and only if the partnership will continue to exist when one member leaves. Of course, B and C have the same termination rights as A, so they could terminate the partnership and start a new partnership. However, termination of a partnership may be impossible if the partnership was established with a fixed/minimum duration.