Q:

Self-deportation of American Citizens from US

It is conceivable that US citizens detained at CBP will self deport to exit  overcrowded CBP detainment facilities avoid lengthy detainments (>20 days).  How would a US citizen's self-deportation affect one's ability to cross borders and return home?
Update:
"Food for thought" for responses:

Upon deportation, why would CBP allow you to re-enter the country with the questioned documents? 
Would CBP not confiscate the questioned documents before deportation?
Citizen is held incommuncado.

There is a claim that 2 of 3 Americans live in the 100-Mile border zone patrolled by CBP:

A:

They can't take his citizenship...
Since he claims to be a born citizen, he has citizenship by birthright and nothing CBP can do can possibly revoke it. 
He can voluntarily renounce his citizenship, but he has to do that through the State Dept. (which CBP is not part of).  And that is an elaborate and expensive process that can't even be done inside the United States. If someone could do it merely by entering without papers and asking for a self-deport, lots of expats would save a lot of money - and that's not gonna happen :) 
...but they could put him to serious inconvenience
In this particular case, CBP found his documents suspect.  Probably because (if it's the case we've seen documented elsewhere) he was with two other people whose entry was illegal, and they had forged documents. 
So most likely, if he agreed to self-deport, CBP would use that as prima-facie evidence that he is not a bona-fide citizen, and therefore, that his papers are faked. They certainly will not give fake papers back to someone who has tried to pass them.  
So the victim would be obliged to go back to SSA, the state, etc. and re-acquire his identity documents.  From outside the country. It's a pretty big chore. 

A:

He's a citizen; his citizenship can't be taken by ICE or CBP, and he can't legally be kept from returning to the US from Mexico by them. He was offered "self-deportation" because ICE was illegally or irrationally detaining him, thinking that his documents were forged or stolen.
He could have "self-deported" in order to simply get out of detention, since it was offered by ICE; but he's a US citizen, so as soon as he was in Mexico, he could simply go to the border and cross with his documents. If CBP kept him from crossing at the border, his lawyer could attest to his citizenship with documents. And any "self-deportation" document he signed could be shown to be meaningless in court, since he's a citizen, and ICE was illegally or irrationally detaining him.

