Final answer:
The right believed to not explicitly exist and which underpinned the Roe v. Wade decision is the right to privacy, leading to a historic Supreme Court ruling that established a woman's right to an abortion as part of a constitutional right to privacy.
Step-by-step explanation:
The right under discussion, which some believe does not exist and has been the basis for the U.S. Supreme Court decision in Roe v. Wade allowing a woman and her doctor to decide about abortion, is the right to privacy. This right is not explicitly mentioned in the Constitution, but has been inferred through interpretation, particularly within the context of the 14th Amendment's Due Process Clause. The landmark 1973 case established a woman's right to an abortion as part of the constitutional right to privacy, which has been one of the most controversial modern Supreme Court decisions and central to ongoing 'pro-choice' and 'pro-life' debates.