Sure. Data that people don't care about enough to be worried about losing--for example, time series data from an unimportant remote sensor. Should this data be recorded at all? Maybe not, but if should then a best-effort recording may be fine. It may even be all that's possible.
I wouldn’t go as far as to say an “unimportant” remote sensor... but I think you’re correct in spirit.
I could think of an instance where you’d like to log data, but the occasional datapoint being missing wouldn’t be terrible. Maybe something like a temperature monitor — you’d like to have a record of the temperature by the minute, but if a few records dropped out, you’d be able to guess the missing values from context. Something like the data monitoring equivalent of UDP vs TCP.
