Great question — answering as the UphillTech team:
It depends on how they are wired. Many strings have two (or more) "parallel" strings of "series-connected" bulbs. Since each of the series strings are independent, then other parallel strings can be safely removed. Remember to carefully insulate the cut ends so that you don't electrocute someone.
Full answer by Richard Crowley: https://diy.stackexchange.com/a/104648 (CC BY-SA 3.0).
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