This happens with dropbox too sometimes. I don't know about Box.
Regarding to DropBox only:
They should not be any important files, and I have understood you can delete them if you want/need to.
I am not sure, but I think these appear if your file is big enough, and you save too rapidly after another save just before. I mean like a second or a couple of seconds after just another earlier save.
They supposedly are some temporary cache or helper files for the cloud sync agent to keep on track with the user hitting panic saves. Might be a symptom of a temporary internet problem too. Sync after save has not received a confirmation, so a temporary file is necessary too keep the promised time line available. There is this feature (DropBox) to go back in time, like a snapshot or Time Machine recovery spot for a file.
That's my understanding, but I really don't know for sure. Those files should not be visible to the user though.
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