My string of fairy lights I have got old and somehow the wire at the end broke and fell off. The lights still work, but is it safe to use with that broken wire?
Your lights may be fine but the end needs to be taped for several reasons. First if 120v or higher an exposed wire could lead to a electrical shock or worse. Second the exposed ends could short together tripping the breaker and causing further damage to the conductors and or insulation. Third if the hot conductor contacts another electrical device that may damage that device and trip the breaker, so putting insulation in the form of tape or wire nuts on the ends will probably make it safe but without a picture it would be difficult to say more.