Fork one: the first beneficiary was an eligible designated beneficiary. Those five categories, covered on their own entry, let a beneficiary take distributions over their own life expectancy instead of clearing the account in a decade. When that person dies, paragraph (e)(3) of the regulation supplies the successor's deadline: the calendar year that includes the tenth anniversary of "the designated beneficiary's death." So the clock starts over, measured from the first beneficiary's death rather than the original owner's. A surviving spouse who draws on an inherited account for twenty years leaves her own beneficiary a fresh ten-year window, and the total period over which the account was emptied can run to thirty years.
Fork two: the first beneficiary was an ordinary designated beneficiary. In that case paragraph (e)(2) already fixed the deadline at the calendar year containing the tenth anniversary of the employee's death. Nothing in the regulation restarts it when that beneficiary dies. Because paragraph (e)(1) requires distribution by the end of the earliest of the years described in (e)(2), (3) and (4), the original deadline continues to bind, and the successor receives an account with whatever time is left on it. An adult child who inherits in year one and dies in year six leaves their own beneficiary four years, not ten.
The third variant, and why it exists. Paragraph (e)(4) covers the account owner's minor child, who is an eligible designated beneficiary only until they reach the age of majority. There the ten-year year is measured from the date the child reaches majority, so the transition is built into the same structure rather than being triggered by a death at all.
Annual distributions do not stop just because the deadline changed. The ten-year rule is a deadline, and it sits on top of whatever annual obligation already applied. Where the first beneficiary was taking life expectancy distributions, the schedule was fixed once and then reduced by one for each elapsed year, so it is a term certain attached to that person's original age rather than a measure of anyone's remaining life. A successor generally continues to take distributions on that same declining schedule, and separately must clear the account by the deadline. Whether an annual distribution is required at all during the years before the deadline depends on whether the original owner had reached their required beginning date, a fact the successor inherits along with the account and cannot change.
What makes this hard in practice is paperwork, not law. A successor beneficiary is named by the first beneficiary, on the custodian's form, after they inherited. Where no successor was named, the account agreement's default applies, which is frequently the beneficiary's estate. That is a materially worse outcome, because an estate is not a person with a life expectancy and the account then has to be administered through probate before anything can be distributed. Anyone who inherits a retirement account has a beneficiary form of their own to complete, and it is the step most commonly skipped, because the account feels like an inheritance rather than an asset that needs planning.