Article 4, Section 3, paragraph 1 - entitled New States; reads
"New States may be admitted by the Congress into this Union; but no new States shall be formed or erected within the Jurisdiction of any other State; nor any State be formed by the Junction of two or more States, or parts of States, without the Consent of the Legislatures of the States concerned as well as of the Congress."
In the case of West Virginia this state legislature requirement was ignored, because Lincoln clearly insisted that the Southern states were in "rebellion" and therefore still a part of the Union, therefore still under the Constitution.
However, if the Southern States were in fact an indepedent country unto themselves, then the "Orphaned" counties of West Virginia petitioning to be admitted to the United States would have been a different matter, in my opinion.