Legal Question in Civil Litigation in California

The reality is that her estate's administrator/executor has the burden of proving the case, and substituting into the case. If the administrator/executor does not do so within a reasonable time, the court on its own or upon motion might dismiss the case without prejudice.

More than likely, the court won't dismiss the case because the third session of the deposition had not been held. Your attorney might want to propound requests for admission and interrogatories that would include the material that would have been covered in the final deposition session. If there is no response, then your attorney could move to have the requests for admission deemed admitted and, in such event you could win the case.

Sometimes, if there is a death and there is no surviving spouse, the estate loses interest in prosecuting a case, unless the result could mean substantial benefit to the beneficiaries. In addition, any claim the decedent had made of infliction of emotional distress no longer exists. If that was the crux of the claim, the potential value of the case is substantially reduced.

There is no requirement that the court dismiss the case because you were unable to take the plaintiff's final deposition.

You don't state what the underlying case is about. Some cases "survive" the death of the plaintiff, and some do not. Further, as Mr. Cohen points out, the representative of the estate is the party to the action now. That requires someone on behalf of the decedent getting appointed under letters testamentary or letters of administration, and then substituting in the place of the deceased plaintiff.