That is not what either document says.
ALL naturalization laws from 1790 forward stated that “IN THE EVENT” the husband/father dies before naturalization is complete, the wife/child does not have to start the process all over again, they become citizens as if the husband/father had lived. SCOTUS cases after the ratification of the 14th Amendment uphold this...
28th Congress, 2nd Session page 129
MR. SAUNDERS’S REPORT ON NATURALIZATION
First, the act of 1802, which repeals all former acts.
It restores the provision of the declaration of intention to three years before application, and a residence of 5 years before admission, and requires proof of good character, renunciation of former allegiance, as well as of all titles or orders of nobility, and an oath to support the constitution; it requires the “registry” of aliens “in order” to become citizens, and the production of the certificate of registration when applying for admission. It further provides for the children of aliens, whether born within or out of the United States
All persons … Chief Justice Waite in 1874:
The words “all children” are certainly as comprehensive, when used in this connection, as “all persons,”
born or naturalized, and subject to the jurisdiction thereof … again Chief Justice Waite in 1874:
Additions might always be made to the citizenship of the United States in two ways: first, by birth, and second, by naturalization…and that Congress shall have power “to establish a uniform rule of naturalization.”
Then 10 yrs later Gray upholds the ruling of the court written by Chief Justice Waite as it pertains to the paths to Us citizenship as it stands under the 14th Amendment:
The distinction between citizenship by birth and citizenship by naturalization is clearly marked in the provisions of the Constitution, by which
“No person, except a natural born citizen or a citizen of the United States at the time of the adoption of this Constitution shall be eligible to the office of President,” and “The Congress shall have power to establish an uniform rule of naturalization.” Constitution, Article II, Section 1; Article I, Section 8. By the Thirteenth Amendment of the Constitution, slavery was prohibited. The main object of the opening sentence of the Fourteenth Amendment was to settle the question, upon which there had been a difference of opinion throughout the country and in this Court, as to the citizenship of free negroes ( 60 U. S. 73; Strauder v. West Virginia,@ 100 U. S. 303, 100 U. S. 306.)
This section contemplates two sources of citizenship, and two sources only: birth and naturalization. The persons declared to be citizens are “all persons born or naturalized in the United States, and subject to the jurisdiction thereof.”; The evident meaning of these last words is not merely subject in some respect or degree to the jurisdiction of the United States, but completely subject to their political jurisdiction and owing them direct and immediate allegiance. And the words relate to the time of birth in the one case, as they do to the time of naturalization in the other. Persons not thus subject to the jurisdiction of the United States at the time of birth cannot become so afterwards except by being naturalized
Thus, if your parents are not citizens at the time of your birth, neither are you and if the parents are naturalized after you are born, so too are you a naturalized citizen.