If you are an undocumented immigrant, it can be a crime to work in the U.S. and not pay taxes on your income. You must pay taxes on income earned from employment in the US, even if you are not lawfully in the US
If you work in the US you are required to file taxes. By filing taxes, you may be eligible for refunds of the taxes that are withheld from your paycheck.
Filing taxes can help with an immigration case. For example, filing taxes is evidence that you are a person with good moral character. It shows that you respect and follow US laws. Showing good moral character is important when applying to become a US citizen and for other types of immigration cases. Filing taxes can also be used to prove the number of years you have lived in the US, which is very important for immigration.
Using false information for work
Even though it is illegal to use false information to get work, for tax purposes there is no difference between legal or illegal income. Illegal income is still taxable and must be reported.
You will not be investigated for crimes or turned in to immigration because you paid taxes on illegal income.