I think that the word “reprieve” would not be a sufficient word to change a person’s immigration status from illegal alien to green card holder absent the person going through the normal hoops that legal aliens have to go through. A reprieve is generally used to commute sentences after conviction and a pardon is used to undo a conviction or prevent a prosecution for an offense already committed.
Obama can try this, but it will be heard in the courts. This would be an unprecedented usurpation of legislative authority
Let’s say he does it. Imagine that he pardons all illegals, and those who hire them, and he says they’re free to stay and work, but must apply for status.
Will someone take him to court? What will happen when they try to take an employer or an illegal to court?
It will be utter chaos.
And he’ll be gone before it’s over.