The concept of Basis Ledavar Ha’asur or a base for a forbidden item, states that something that is normally permitted to be moved on Shabbat that serves as the base of Muktze becomes Muktze itself. The Shulhan Aruch (O.H. 277:3) writes that if one lit Shabbat candles on a tray and the candles were later somehow moved (such as if they were knocked down, moved by a non-Jew or the like), one would not be able to move the tray. Since the candles were set aside on the tray before Shabbat, the tray is rendered into a Basis and is considered as part of the candles, and is therefore also Muktze. It should be noted that if Muktze is placed on a base during Shabbat it does not become a Basis, such that if the Muktze were somehow moved off, one would be able to move the base.
One way to circumvent the issue of a base becoming Muktze is to place something that is not Muktze on the tray before Shabbat. In the case of a tray which supports candles, some women place a ring on the tray so that if the candles are somehow moved, they would later be able to pick up the tray on Shabbat.
One anecdote that illustrates the concept of Basis is the Ramada Hotel case: The story goes that a chair was used as an ad hoc support for candles at a hotel hall as no other surface was readily available. The non-Jewish workers later cleared the candles from the chair and moved the chair back with the other chairs in the room. Since the chair served as a Basis for the candles, the chair itself became Muktze, yet the Jewish guests did not know which chair was used. As such, by moving any chair one could potentially have been moving the chair that was a Basis. Although, normally one can evoke the principle of Bitul (nullification), in this case since after Shabbat the chair is once again permitted it is considered Davar Sheyesh Bo matirin (i.e: one should not rely on nullification when it will be permitted the next day). Rav Ovadia Yosef (Hazon Ovadiah Shabbat 3:pg 133) raises this point and quotes the opinion of Rabbi Yehezkel Landau ( Tziyun Lenefesh Haya, Pesahim 9b) who says that unlike food, which can be eaten the next day, the seat is needed immediately and therefore Bitul would work. Therefore, there would be no issue in moving a chair in that room.
Summary: If an item that is considered Muktze on Shabbat is placed on a base before Shabbat, the base becomes Muktze as well and cannot be moved on Shabbat.