First of all, someoneu2019s visa being expired does not mean they are undocumented. US visas are solely for entry, the visau2019s expiration date is the last day one can use that visa to enter the US, it has nothing to do with how long one can stay in the US. One can enter the US on the day the visa expires, and be admitted for months or years afterwards.Second, you fill out your W-4 withholding form based on your marital status and tax situation. Your spouseu2019s immigration status is not relevant to any part of the W-4 form. And generally, the tax laws apply the same way to people residing in the US, regardless of whether they are documented or undocumented. You and your spouseu2019s tax returns would be computed and filed the same way regardless of whether you and your spouse are documented or undocumented.