What is the biblical basis (if any) for the many reports by people about being sexually assaulted at night by succubus/incubus?
I believe that there very few, if any Christian denominations that explicitly teaches that a demon succubus or incubus exist.
It is a little far fetched, but I give it a reasonable try at answering the question.
First of all, the Book of Tobit has an interesting story about Tobias, Sarah and the demon of lust, Asmodeus ("the worst of demons")!
The Book of Tobit is listed as a canonical book by the Council of Rome (A.D. 382), the Council of Hippo (A.D. 393), the Council of Carthage (397) and (A.D. 419), the Council of Florence (1442) and finally the Council of Trent (1546), and is part of the canon of both the Catholic Church and Eastern Orthodox Churches. Catholics refer to it as deuterocanonical.
Augustine (c. A.D. 397) and Pope Innocent I (A.D. 405) affirmed Tobit as part of the Old Testament Canon. Athanasius (A.D. 367) mentioned that certain other books, including the Book of Tobit, while not being part of the Canon, "were appointed by the Fathers to be read".
Before the 1952 discovery of Aramaic and Hebrew fragments of Tobit among the Dead Sea Scrolls in a cave at Qumran, scholars believed Tobit was not included in the Jewish canon because of late authorship, estimated to A.D. 100. Qumran fragments of the text, which were copied between 100 B.C. to A.D. 25, evidence a much earlier origin than previously thought. These fragments evidence authorship no later than the 2nd century BC and, likely, contemporary with the date ascribed, by modern scholars, to the final compilation of the Book of Daniel, which did attain canonical status.
This book tells the story of Tobit, a righteous Israelite of the tribe of Naphtali, living in Nineveh after Sargon II had deported the northern tribes of Israel to Assyria in 721 B.C. In the two Greek versions, the first two and a half chapters are written in the first person; in the Vulgate version, they are written in the third person. Tobit, raised by his paternal grandmother, Deborah, remains loyal to the worship of God at the temple in Jerusalem, refusing the cult of the golden calves that Jeroboam, king of the northern kingdom of Israel, set up at Dan. He is particularly noted for his diligence in attempting to provide proper burials for fallen Israelites whom Sargon's successor, Sennacherib, has slain. For this behavior the king seizes his property and exiles him. After Sennacherib's death, Tobit is allowed to return to Nineveh, where he buries a man who has been murdered on the street. That night, he sleeps in the open and is blinded by bird droppings which fall into his eyes. His blindness subsequently leads him to falsely accuse his wife, Anna, of stealing a baby goat she had received as partial payment for work she had done. This strains his marriage and, ultimately, he prays for death.
Meanwhile, in faraway Media, a young woman named Sarah has prayed for death in despair. The demon of lust, Asmodeus ("the worst of demons"), abducts and kills every man Sarah marries on their wedding night before the marriage can be consummated. God sends the angel Raphael, disguised as a human, to heal Tobit and free Sarah from the demon. - Book of Tobit
The only other possible source that may again be a remote answer involves the Nephilim from the books of Genesis and Ezekiel. The possibility only exists as to how some interpret Sacred Scripture.
The Nephilim (Hebrew: נְפִילִים) were the offspring of the "sons of God" and the "daughters of men" before the Deluge, according to Genesis 6:1-4.
A similar or identical biblical Hebrew term, read as "Nephilim" by some scholars, or as the word "fallen" by others, appears in Ezekiel 32:27.1
When people began to multiply on the face of the ground, and daughters were born to them, the sons of God saw that they were fair; and they took wives for themselves of all that they chose. Then the Lord said, "My spirit shall not abide in mortals forever, for they are flesh; their days shall be one hundred twenty years." The Nephilim were on the earth in those days—and also afterward—when the sons of God went in to the daughters of humans, who bore children to them. These were the heroes that were of old, warriors of renown. — Genesis 6:1–4, New Revised Standard Version
The word is loosely translated as giants in some Bibles and left untranslated in others. The "sons of God" have been interpreted as fallen angels in some traditional Jewish explanations.
According to Numbers 13:33, they later inhabited Canaan at the time of the Israelite conquest of Canaan.
The Lord said to Moses, "Send men to spy out the land of Canaan, which I am giving to the Israelites" ... So they went up and spied out the land ... And they told him: "... Yet the people who live in the land are strong, and the towns are fortified and very large; and besides, we saw the descendants of Anak there." ... So they brought to the Israelites an unfavorable report of the land that they had spied out, saying, "The land that we have gone through as spies is a land that devours its inhabitants; and all the people that we saw in it are of great size. There we saw the Nephilim (the Anakites come from the Nephilim); and to ourselves we seemed like grasshoppers, and so we seemed to them." — Numbers 13:1–2; 21; 27–28; 32–33. New Revised Standard Version.
And now let us look at what the Sons of God may mean:
Sons of the God (Hebrew: בני האלהים) literally: "sons of the Gods") is a phrase used in the Hebrew Bible and apocrypha. The phrase is also used in Kabbalah where bene elohim are part of different Jewish angelic hierarchies.
And it came to pass, when men began to multiply on the face of the earth, and daughters were born unto them, That the sons of God saw the daughters of men that they were fair; and they took them wives of all which they chose. And the LORD said, My spirit shall not always strive with man, for that he also is flesh: yet his days shall be an hundred and twenty years. There were giants in the earth in those days; and also after that, when the sons of God came in unto the daughters of men, and they bare children to them, the same became mighty men which were of old, men of renown. — Genesis 6:1–4, KJV
The first mention of "sons of God" in the Hebrew Bible occurs at Genesis 6:1–4. In terms of literary-historical origin, this phrase is typically associated with the Jahwist tradition.
This passage has had two interpretations in Judaism:
Offspring of Seth: The first references to the offspring of Seth rebelling from God and mingling with the daughters of Cain are found in Christian and rabbinic literature from the second century CE onwards e.g. Rabbi Shimon bar Yochai, Augustine of Hippo, Julius Africanus, and the Letters attributed to St. Clement. It is also the view expressed in the modern canonical Amharic Ethiopian Orthodox Bible. In Judaism "Sons of God" usually refers to the righteous, i.e. the children of Seth.
Angels: All of the earliest sources interpret the "sons of God" as angels. From the third century BCE onwards, references are found in the Enochic literature, the Dead Sea Scrolls the (Genesis Apocryphon, the Damascus Document, 4Q180), Jubilees, the Testament of Reuben, 2 Baruch, Josephus, and the book of Jude (compare with 2 Peter 2). This is also the meaning of the only two identical occurrences of bene ha elohim in the Hebrew Bible (Job 1:6 and 2:1), and of the most closely related expressions (refer to the list above). In the Septuagint, the interpretive reading "angels" is found in Codex Alexandrinus, one of four main witnesses to the Greek text.
Rabbinic Judaism traditionally adheres to the first interpretation, with some exceptions, and modern Jewish translations may translate bnei elohim as "sons of rulers" rather than "sons of God". Regardless, the second interpretation (sons of angels or other divine beings) is nonexistent in modern Judaism. This is reflected by the rejection of Enoch and other Apocrypha supporting the second interpretation from the Hebrew Bible Canon.
According to Scripture “sons of God” means “persons who are begotten independently of any creature’s decision”. All angels can appropriately be called “sons of God”, but not all characters called “sons of God” in the Bible can appropriately be considered angels. The “sons of God” in Genesis 6:1-4 are undoubtedly human, and it is fitting to consider that they were created directly by God through transformation of human-like animals into persons.
Who was the son of Enos, who was the son of Seth, who was the son of Adam, who was the son of God. - Luke 3:38
Thus if the Nephilim were the descendants of the Sons of God (sons of Adam) and the "daughters of men" surely not all of them were evil. Some of them would have had good and upright souls. Someone could ultimately link them as being succubuses or incubuses, but that is really stretching it!