Charge a supercapacitor in 4-20 ma circuit
In theory, it is simple. You connect your 4-20 to the supercap with the correct polarity, and then the circuit will drive a constant current in to charge it. BUT it will raise the voltage to whatever is necessary to drive that current, which will almost certainly be greater than 2V7, and will damage the supercap. So, protect it with a zener across the terminals so voltage cannot exceed 2V7. BTW, shorting out a 4-20 current loop will not damage it.