What would have happened if the Union and Confederates decided to declare a stalemate and sign a peace treaty? To clarify, no side is gaining any traction on the other, and they declare a draw. If the borders remained like shown below, what would have happened?
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Confederate success was predicated upon an actual "Treaty of Peace" between the United States and the Confederate States, according to Confederate paper money...
Without such a treaty there would be no payout evidently...
The United States would have had to modify the Constitution to establish any kind of Treaty with the CSA, as it would have required the United States to recognize it as an agency to do so. The Constitution forbids the US Government from allowing any Confederacy of its States...
Because of the above, the United States never recognized the Confederacy in any political sense. And because the Southern State governments were in opposition to US jurisdiction, etc., the US Government did not consider them as entirely legitimate republican governments either.
So given these Constitutional issues, if there were a complete military stalemate at some point, the United States would have just ceased military action and perhaps parked troops, etc. on the border with the Confederacy, etc. But so long as the United States Government existed, under the Constitution, many in the North considered it inevitable that it had to press the Union cause without cessation...
Such a situation of a military stalemate, in which military action within the Confederate States ceased, would not evidently have had any effect on the Constitution and the laws unless the US Constitution was in some manner modified or abandoned by the States.
In Jefferson Davis' hearing in federal court in 1868 his lawyer Mr. O'Conor argued against the treason charge against his client, noting that he had just passed through a Civil War; and alluded to a hypothetical that had the Confederacy survived intact for some decades, employing all the attributes of a de facto government so that should the United States thereafter have restored its jurisdiction, it surely couldn't have accused Davis' descendants of treason, etc. for abiding their powers that be where a federal jurisdiction was not manifest... viz. so long as the US Constitution remained in effect, the children of the Confederacy would have been United States citizens per the United States, irrespective of the interruption of the laws of the Union therein.
Anyways, Thomas Jefferson in 1798 opined that a sectional scission of the Union would lead even Southern States to eventually target each other, so they could not last too long...
And many former Confederates presumed that had the conflict with the United States Government ceased before the collapse of the Confederacy the Southern States might have turned upon their Confederacy or each other. As early as April, 1861 there were rumblings of secession from the Confederacy...
And even during the wars' course...
Robert Underwood Johnson opined in the early 20th Century on the subject:
Johnson is quoting former Confederate General Roger A. Pryor, who opined in 1889:
General William T. Martin of Mississippi, from 1865:
General E. Porter Alexander of Georgia: