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The UnioinListState is more complex. A common usage pattern is to implement a "broadcast" state by storing state on a single subtask.  Afterwards, when initializing subtasks the single copy of the state would be distributed to all subtasks. Another common pattern is to use a UnionListState to create a global view. It is used for example to share information about offsets of partitions which has been consumed so far. This lets us restart from the given offset if after restore a partition is assigned to a different subtask than originally. Such a logic can only be implemented with a merged state of all original subtasks If a part of subtasks are finished and we only keep the remaining state in the checkpoint. This can obviously loose important bit of information, or even the entire state in case of described implementation of broadcast state. However, since the UnionListState is on the way to be deprecated and replaced by the OperatorCoordinator.

For the time being, we could first have a temporary fix by asking the tasks of operators using UnionListState to wait for each other to make sure the snapshot of the operator must be complete. We would decline checkpoints if some of all the tasks reported they have called the finish()  method, but some have not received notifyCheckpointComplete yetwill allow for a situation that if an operator checkpoints UnionListState, it can only finish all at once. We will decline checkpoints if not all of the tasks called finished and received notifyCheckpointComplete .

Based on the above discussion discarding the final states of the finish tasks would only change behavior for a very little fraction of the possible existing jobs whose non-source operators have special logic on initialization or endOfInput, and these jobs could also be modified to keep the current behaviors.  Therefore, we lean towards option 3, which simplify the implementation and leave more room for optimization in the future. 

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