By their own words, the drafters of the 14th amendment did not intend that it would convey citizenship to foreigners. The children of foreigners here illegally are themselves illegal foreigners.
Being arrested doesn't make you "subject to the jurisdiction". You have to be "subject to the jurisdiction" to be arrested. What the phrase means is subject to the law. People who are not subject to the jurisdiction have some form of immunity, or are otherwise not bound by our law. Mainly, diplomatic immunity and invading soldiers.
"By their own words, the drafters of the 14th amendment did not intend that it would convey citizenship to foreigners."
By the words of the 14th (and the pre-existing law) being born here makes one a citizen.
"The children of foreigners here illegally are themselves illegal foreigners."
Unless they are born here, in which case they are citizens.