"...how does an organization ensure the task still gets done?"

With something almost stupidly simple and low-tech: checklists.

(I'm reading "The Checklist Manifesto" right now, and the points it makes seem to fit perfectly with everything you mention.)

An year is enough time for everybody that knows about the checklist to leave.

We resolved this issue at my last company with sufficiently large mailing groups for cert renewal reminders. Once you get to 12 people on a mailing list, with new employees being added all the time, it's hard to miss. Usually a manager on that list is pinging people about it. There is the chance of the tragedy of the commons occurring, but I never saw it.

Once you do this, the only checklist that matters are procedural checklists to add a new client or new cert to the renewal notification list. When you use a standard group email for all cert purchases, that one becomes tough to miss.

In my 7 years of being involved, we never missed a cert renewal with this process for ~300 client sites with multiple or wildcard certs.

Put "make sure someone else knows all this person's checklists" on the employee exit checklist.

Put the checklist on the home page of the company website!

There should be a separation between the things that need to get done and the people that do them. As in, tasks should be created first and then assigned.

Surely tasks are performed by and assigned to roles, not individuals (who just happen to be in those roles at some moment in time). If a role disappears, e.g. in redundancy, then the role's tasks are evaluated for either transfer to a role that remains, or being discarded.

Just one : Emacs orgmode