So if "killed mid-operation" must be supported then I don't see how many algorithms can be said to make progress. Take for example the Lamport SPSC queue[1], if the producer gets killed mid operation between steps 4 and 5 of the push operation. Then the data is in the queue but the consumer is blocked from ever seeing it with this line of reasoning. The Lamport SPSC queue is considered wait-free by the concurrency community I know. I base my reasoning on this. What if the producer takes a pause for a long time between steps 4 and 5 before continuing?
However if to be wait-free an algorithm must allow all other threads to continue using the data structure, not just continue making progress in other ways by being non-blocking and completing in a finite number of steps, then I stand corrected.
If wait-free must include coping with any thread being killed mid operation is there a term for being lock-free but also having all threads not block and complete in a finite number of steps for their interaction with the algorithm?