It's possible to design pathological equipment that fails under low voltage conditions, as an exercise in 'what not to do', but generally any design that has started life like this will have been caught by testing, and modified before it gets to customers, so that it 'fails safe' under low voltage.
A good way would be to have a heat generating mechanism that works at all voltages, and a cooling mechanism that fails. For instance, a motor cooled by a fan on its own shaft, that fails to turn at low voltage.
A kettle is such a simple device, that my first thought was 'yes, you can make coffee at any any voltage'. However, if you leave it unattended, the automatic switch-off might require a certain minimum rate of steam flow to send enough steam down to the thermal switch (mine does), so it could boil dry. But then all kettles (should) have an overheat cutout as well, that will switch off if boiled dry.
There's an interesting class of motor that will overheat if run at too low a load! Think about that one for a moment. It's a particular type of induction motor, and at low load the speed rises to near synchronous, so the slip frequency drops so low that the armature saturates and draws excessive current. Not all induction motors behave like this.