- I can't think of any 3-wire voltage divider application that would need a current limiting resistor like what you describe.
On further consideration, there are some applications where you could wire a resistor in series with a potentiometer.
I actually do this a lot - it allows you to set a base value above zero, for the range you want to control. If this is to ground, it also has important safety considerations (as the current draw will increase as pots' resistance falls towards zero, which would then be a dead short, meaning the circuit' power draw may increase significantly).
For example, you want to have the resistance to ground vary between 500R and 1500R, so you use a 500R resistor in series with a 1k pot.
If you had 5v for potentiometer power, but needed to step it down to 3.3v for a gamepad hack or a RasPi GPIO input, you could use the resistor to drop 1.7v and the pot to drop 3.3v.
Using a voltage divider for this is going to waste a lot of power. Instead, I'd suggest using a Low-Drop Out (LDO) 3.3v voltage regulator like the MCP33002e, which is available in through-hole format (TO-92-3, long legs) so convenient for hobbyists. They are quite efficient for low-current applications (<300mA iirc). It would keep the voltage and current more consistent. There are many alternatives and you can get them for many different voltage outputs.
- Same process could also be used to step down a 12v power source by dropping 7v with a resistor, leaving 5v for the pot.
Again, using a resistor to lower your power voltage seems like a bad idea? Wouldn't you be better off using a voltage regulator chip like the good-old 7805? Or just using a 5v power brick?
Another possible application would be a limited range LED dimmer circuit.
- The resistor would drop just enough voltage to forward bias the LEDs (dim) and the wiper would allow you to adjust the LED voltage from dim to bright.
Bear with me

The way I understand it, and observe it to happen, is this:
The resistor drops the current to the LED, which lowers the voltage as well, but the final voltage drop happens over the LED (assuming you wire it resistor->LED), so long as there is enough minimum current to light the lamp. So, you'd wire the pot in series with the (minimum) resistor and LED, with only two terminals from the pot attached. No third wire to ground.
For example, an LED with 2v Vf will always drop 2v, regardless of what current limiting resistor you use, so long as there is enough current to light the lamp.
This also means that the voltage drop across the resistor+pot must always be equal to Vcc - Vf, so long as the resistor is at or above the minimum for that LED. So, although the resistor+pot does make voltage fall, it is more a current limiter than voltage divider. Current is the variable making the LED brighter or dimmer.
Power supply (Vcc) -> current limiting resistor -> pot -> LED -> GND
You can wire it LED->resistor and it works the same way, just flipping the voltage drops (current remains the same).