As I understand it, this is mainly handled through the LPA’s Key Person and GP Removal provisions.

For a solo GP, the GP is typically the key person. If the GP can no longer serve, the LPA can trigger a suspension of new investments and give LPs a process to approve a successor or wind down the fund. If LPs simply lose confidence, the LPA can also provide for GP removal, either for-cause or no-fault, depending on the negotiated terms.

So the fund doesn't necessarily die with the GP, the LPA should define the continuity and removal mechanisms upfront.