What would the voltage across the resistor be? What would its polarity be? I don't see anyway for KVL to not be violated.
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An ideal circuit diagram has an associated set of equations. In this particular case, the resistor is irrelevant to the KVL equation which is $$1V = -1V$$
which is nonsense.
Just as one can write inconsistent mathematical equations, one can draw inconsistent ideal circuit diagrams (which are simply a different representation of a system of equations).
Here's another example which is, in fact, the dual of the given circuit:
The KCL equation for this circuit is
$$1A = -1A$$
which is, again, nonsense.
So, there are rules for ideal circuit diagrams including but not limited to
don't place ideal voltage sources in parallel (or short-circuit a voltage source)
don't place ideal current sources in series (or open-circuit a