The government is non other thing that a representation of the people, and if the people wants to grant Citizenship or Permanent Residence (Green Card) to a foreign citizen, the government would be doing just what the people wants to do.
Therefore, if enough US Citizens are in favor of granting such rights to a particular person, such petition should be granted, and citizenship or permanent residence awarded to such deserving alien person.
I'm proposing 5,000 signs for such a petition to be granted, but that number can be changed to a more suitable number for the majority of the people to agree with it.
Of course this should not eliminate any of the other ways a foreign citizen can be granted such rights.