The short answer is - yes, there are a bunch of ways to be legally in the United States without a green card. These tend to be temporary, or contingent on other things, so harder to track and produce immediate evidence of.

The longer answer is, it doesn't matter. Deportation is a tool in the government's tool kit for dealing with those who entered the country illegally - but Deportation is a process, with steps, due process and it requires the ability for the potential deportee to argue their case to an immigration judge. Being grabbed by masked thugs off the street, taking a brief layover in Louisiana while they fuel the plane and then being deported to a torture facility in El Salvador without so much as ever speaking to your lawyer is a contravention of your rights. Your human rights, your 5th Amendment rights, take your pick.

Kilmar Abrego Garcia, for example, was never formally granted asylum. He missed the filing deadline of one year. However, in his original deportation trial he showed significant evidence and credible testimony that he had fled El Salvador to escape being forced to join the gang that was shaking down his family for protection money. The only reason he wasn't deported after that original hearing was that a Judge granted him hold order - stating he specifically could not be deported to El Salvador because his life would be in danger. It's unlikely he has any simple card or document that shows that order he could carry with him. In direct violation of that order, ICE sent him anyway. He's almost certainly dead.

So you are walking down the street, being a super careful to always have your passport. Then a van pulls up and stuffs you in it. You declare you have a passport and are a citizen, but they don't care. You didn't get due process to show your documentation because they "mistakenly" put you down the "no due process" path.

It isn't really possible to assure due process for only select people, either everyone must have it or else anyone could have due process denied under a claim that they belong to the "no due process" class.

Due process does not necessarily mean leniency, it just means a reasonable process and a chance to be heard and present your documentation and such. Without that guarantee, there's no accountability of the enforcers and no guarantee you even can present your documentation.