Responsibility to complete the year-of-death RMD transfers to the beneficiary(s) upon the death of the IRA participant. The result is that whatever portion of the year-of-death RMD was completed by the participant before death goes on the participant's final tax return and is the only portion that the decedent was required to complete. No Form 5329 Part IX is ever to be included with the decedent's final tax return. The remainder of the year-of-death RMD that is completed by the beneficiary(s) goes on the beneficiary(s) tax return(s).
The responsibility of the beneficiary(s) to complete the remainder of the year-of-death RMD is addressed in CFR 1.401(a)(9)-5(d)(1)(i): https://www.ecfr.gov/current/title-26/chapter-I/subchapter-A/part-1/subject-group-ECFR6f8c3724b50e44...
Regarding whether a complete distribution of the inherited IRA(s) satisfies the RMD, the point of RMDs is to prohibit excess accumulation in the IRA(s). With nothing left in the IRA(s) after a full distribution, there is no accumulation and therefore no excess accumulation, so the requirement has been satisfied. Although I doubt that it applies in this situation, that holds even if, due to investment losses, the total amount distributed during the year to the participant and the beneficiary(s) combined is less than the RMD calculated from the previous year's year-end balance. In that case you can either simply report as the required amount the amount actually distributed, or, if you enter a higher required amount based on the calculation from the previous year's year-end balance, resulting the Form 5329 Part IX being included in your tax return, you can request a penalty waiver on the portion not taken due to reasonable cause, the reasonable cause being that there is nothing left to distribute.
