It is possible for people who awaiting processing in the U.S. to travel abroad using a U.S. Citizenship and Immigration Service document called advance parole – but in your case it would be extremely unwise to do this as you could jeopardize your future here if you leave without first being approved for permanent resident status through your marriage.
Advance parole is available for those who are adjusting status while in the U.S. from non-immigrant to permanent resident. While an adjustment of status case is pending, an applicant is not permitted to leave the U.S. without advance parole. Departing without parole is considered to be an abandonment of the case, and the applicant could be considered inadmissible when attempting to re-enter the U.S.
Advance parole must be applied for using USCIS Form I-131. Once it is issued it allows the holder to leave the U.S. and be paroled back in, without jeopardizing the pending adjustment of status case.
However – and this is a big however – those who have accumulated a period of undocumented residence here should not avail of advance parole. In your particular case, you’ve married an American and as such you’re eligible to adjust your status from undocumented to permanent resident. This process can take a few months, depending on where in the U.S. the case is being processed.
But if you leave the U.S. during this time and try to re-enter, even with advance parole, the overstay will cause you great difficulty and could render you ineligible to adjust status.
Here’s succinct advice on the matter from the USCIS website: “If you depart the U.S. after accruing certain periods of unlawful presence in the U.S. (time spent in the U.S. illegally) you may be barred from admission for either three years or 10 years, depending on the amount of unlawful presence an individual has accrued. Any departure from the U.S. may trigger this ground of inadmissibility, even if you have obtained an advance parole document . . .
“(The) card authorizes parole, not admission, to the U.S. Parole is not an admission or ‘entry.’ If you obtain this card, you may use it to travel abroad and return to the U.S. . . . issuance of an advance parole document does not guarantee that (Customs and Border Patrol) will parole you into the U.S. If parole is granted, you will be permitted to come into the U.S. as a parolee, but will not have been ‘admitted.’
Individuals who have been unlawfully present in the U.S. and subsequently depart and seek re-entry through a grant of parole may be inadmissible and ineligible to adjust their status.”
If you departed the country and were paroled back in with the document, you’d be subject to a 10-year bar from the U.S. You could apply for a waiver to remove the bar, but they are difficult to obtain.
After consulting a few immigration experts about your letter, the advice is unequivocal – remain in the U.S. until your case is approved. Of course it’s very unfortunate when a family member abroad is ill, but you would be putting your future at grave risk if you were to leave.