It depends on whether the material is ohmic or non-ohmic.
If it is ohmic, then it will obey Ohm's Law, and its resistance will remain constant if the current decreases.
If, on the other hand, it is non-ohmic, it will not obey Ohm's Law and, if the temperature of the conductor falls (assuming it is a metallic conductor) due to the fall in current, then its resistance will fall too.
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