Wikipedia, the online encyclopedia says this about Karaite Judaism:
Karaite Judaism or Karaism is a Jewish denomination characterized by the sole reliance on the Tanakh as scripture, and the rejection of the Oral Law (the Mishnah and the Talmud) as halakha (Legally Binding, i.e. required religious practice). The word "Karaite" comes from the Hebrew word קְרָאִים (Standard Qəraʾim Tiberian Qərāʾîm), meaning "Readers (of Scripture)." This name was chosen by the adherents of Karaite Judaism to distinguish themselves from the adherents of Rabbinic Judaism.
Doing a Google search will several web sites explaining the beliefs and history of the Karaite Jews.
But the interesting thing, as far as our subject is concerned, that in rejecting the Rabbinic and oral traditions whenever in conflicts with the teaching of the Tanakh (the Old Testament) the Karaites reject the position of most modern Jews that the righteous dead "go to heaven" and believe the dead are "sleeping." Here is a link to one of their pages explaining their position.
Yes, the Old Testament supports the position that the dead are at rest, awaiting a call by God to awake, arise, and enter His Kingdom!
In relying on only the scriptures of the Old Testament (the Hebrew Tanakh) they await the arrival of the Messiah when the dead shall be raised and judged. The Messiah will sit on David's Throne, in the Temple at Jerusalem. This will usher in the Messianic era when all the world will worship the one true God.
Because of their total reliance on the Tanakh they strongly reject evangelic attempts to proselytize and, perhaps, are more anti-Christian than most Jews. This in not only because they reject Jesus as the Messiah, but because they accuse Christians of doing away with the Old Testament Law.