They survive. Tasks are persisted with their schedules and state, so process, container, and host restarts resume work instead of losing it, without duplicating what was already done.
This is the difference between a runtime and a chat product. A job that dies with a deploy is a toy; Heidi's scheduler is durable by design.
Midway failures are equally honest: attempt logs record every try, and receipts show exactly how far the work got. Details at falkster.ai/answers/failed-actions.