If the transmission voltage is increased, then the load resistance is increased, so that the power is kept the same. The load resistance is either increased by putting a transformer in the way, or by redesigning the load. If a transformer is used, it's actually the impedance not the resistance that is increased, but the concept is the same.
Because the power is the same, the current is less if the voltage is bigger. If the same cable is used, the resistance of the cable is the same. Less current means less voltage drop in the cable.
For example, a vehicle headlight is 55 W. It can't be more, or the casing would melt.
55 W bulbs are available at 12 V for cars or 24 V for trucks. The 24 V ones are made with longer, thinner filaments. The resistance of the 12 V ones is 12 x 12 / 55 = 2.62 Ω. The resistance of the 24 V one is 24 x 24 / 55 = 10.47 Ω
If the cable has a resistance of 0.1 Ω, the voltage drop at 12 V is 55 / 12 x 0.1 = 0.45833 V and 2.1 W of power is lost in the cable.
At 24 V, the voltage drop is 0.2292 V and 0.525 W of power is lost in the cable.