Limiting current WITHOUT dropping voltage
Presumably you are okay with a small drop, provided it is less than 0.5V. 

Here is a circuit that will limit at 100uA and will drop less than 100mV before it limits.







simulate this circuit &ndash; Schematic created using CircuitLab

The MCP6001 is an inexpensive rail-to-rail input/output op amp that will operate from a 5V supply. The op-amp will saturate at ground until the load current reaches about 98uA nominally (with the values shown). The supply thus 'looks like' 5V with ~1K in series (the MOSFET contributes less than 10 ohms with Vgs =-5V), so it will drop between 0 and 100mV for load resistances of infinity down to 50K. 

For lower load resistances the circuit regulates the output current to ~98uA. 

The circuit draws about 200uA from the 5V supply, in addition to the load current of 0~100uA.