Voltage across a resistor?
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:







simulate this circuit &ndash; Schematic created using CircuitLab

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
current source)