Good question, and the honest answer is that it depends on the job, and the design should say which.

When the timeout fires, that run has already stopped, so a late approval can’t resume it. For anything where the inputs age (market data, feeds, row counts), I’d have the late approval start a fresh run with fresh inputs. Approving evidence that is now stale is the riskier choice. For jobs with a snapshotted, versioned input, a resumable run with reminders and escalation before the timeout can make sense. The point is to decide it per workflow and write it down.

My broader idea is the same either way: use AI to build custom tools for repeated work, so the work still runs when the AI doesn’t. A good example is stock analysis. People reuse one prompt and swap the ticker. Build the analysis once as a tool, and each new ticker costs no model call. I did that with stockverdicts.com. Keep the model for the ambiguous parts.