The reason for low unemployment in Mexico is a lack of social safety net. Starvation is a strong motivator for taking any job available—— or swimming a river and taking any job available. Do away with lifetime unemployment and food stamps and see how quickly the unemployment and illegal immigrant problems shrink.
The only 'lifetime' unemployment I know of is being independently wealthy, winning the lottery, etc.
The major cause of our 'illegal' immigrant problem is the MINIMUM WAGE Law.