What is the resedency period for illegal immigrants residing in Illinois and the what is the penalty?

Question

and what is the penalty for using a false social security number( one which belongs to someone else?

Answer 1

There is no residency period for illegal immigrants. Using a false social security number is a federal crime even if it does not belong to someone else. That said, the leaders of the current congress are on record as supporting amnesty and not punishing them at all. This is one of the few issues on which they seem to agree with the President.
I am aware the congressional leadership is opposed to the word amnesty, but their stated policies fill the definition of amnesty.

Answer 2

Someone else using your Social Security number with your knowledge and consent would constitute Conspiracy to commit Fraud against the United States and Fraud against the United States. The penalty would probably be deportation for the illegal immigrant and Prison for you.

Look at it like a simple math problem.
Conspiracy to commit Fraud = 1
Fraud = 1
Prison = 2
1+1=2