That generally gets broken into several separate things:

1. Current density for a defined element - Usually a max current is defined for a given geometry of a given circuit element.  Lets say a 1u wide resistor is limited to 100uA, so if you go to a 2u wide resistor, you can put  20uA in it. (numbers are not real)

2. Electromigration current and voltage rules. These are unique to a foundry process. See the PDK and associated documentation.

3. Thermal elevation: Wattage dissipated in the chip (usually done in degrees C per watt as part of the package rating) will lead to a thermal limit violation. If it runs in a 30C environment, and the package thermal rating says you are elevating the chip 90 degrees means the chip is at 120C inside the package. If the foundry says the silicon is only good to 100C you have problems.