Originally Posted by Demise

Presidential waiver. The president could well authorize USCIS to grant pardons for immigration violations which prevent people from adjusting status. While he cannot throw green cards at people, he can clear the way for anyone otherwise seeking adjustment of status.

So what could be done (using a few cases to illustrate).
You entered US illegally 10 years ago.
You found an employer willing to sponsor you (or are otherwise eligible to adjust status aside as an immediate relative).
USCIS waives your previous illegal presence under a pardon EO before you leave to go to the consulate.
Once your priority date is current you leave US (with no re-entry ban) undergo consular processing, get your immigrant visa, and return to US.

You entered US illegally 12 years ago, were caught on the border, given a hearing date, and were never seen again. You were ordered removed in-absentia.
You married a US citizen.
USCIS grants you parole in place as a part of your adjustment application.
USCIS pardons you from being ordered deported.
You adjust status as an immediate relative.

You overstayed your visa 3 years ago.
You win the green card lottery.
USCIS pardons your previous illegal presence.
You leave US, visit the US consulate abroad, pick up an immigrant visa as a lottery winner and return to US.

Only things needed here would be two:

EO from the president which says:
"I authorize the Secretary of Homeland Security to grant presidential pardons on my behalf to any person who has committed immigration violations which make them inadmissible to United States."


New USCIS form "Request for immigration pardon(s) and/or deferred action and/or parole".
The form listing the following:

Part 1:
(check box) I am seeking pardon(s) because (check one):
I am inadmissible and:
a) I seek to adjust status to that of a permanent resident in United States.
b) I seek to undergo consular processing for an immigrant visa abroad.
c) I seek to obtain a non-immigrant visa in the following category: ____
d) Other (please specify): ____________________

I believe to be inadmissible due to the following reasons and no others, for which I seek pardon(s) (check all the apply):
(Full list of inadmissibilities to US, akin to that found on an application for U-visa will be here).

Part 2:
(check box) I am seeking deferred action because (check all that apply):
a) I have a pending or approved immigration petition for which the priority date is:
i) Current
ii) Not current
b) My removal from US would cause hardship to a US citizen or permanent resident family member(s).
c) My removal from US would cause hardship to myself.
d) I seek to extend previously granted deferred action.
e) Other (please specify): _____________________

If you checked section part 2(a) please enter information of the petition:
Category: ________
Priority date: ________
Approval date: ________ (check box) Not yet approved.

If you checked section part 2(b) please enter the information of the family members (multiple of these):
Name:
Relationship:
Status: (check box) USC (check box) LPR
SSN:
Address:
Place of birth:
If LPR, country of citizenship:

Part 3:
(check box) I seek parole in place because (check one):
I am an immediate relative of a US citizen US military member.
I am an immediate relative of a US citizen who is not in the military.
Other (please specify): _______

[Signature section here]