The Shulhan Aruch, in Siman 309, outlines the Halachot of an item which serves as a "Ba'sees L'davar Ha'asur"-a base for a forbidden Mukse item. For example, a tray, which is not inherently Mukse, becomes Mukse, if money is deliberately placed upon it before Shabbat and remains there during Ben Ha'shmashot (Twilight=the 15 minutes after sunset). Even if the money is somehow removed from the tray during Shabbat, perhaps by the non-Jewish maid, the tray remains Mukse! There would be no point trying to shake the money off the tray, because even if the money would be removed, the tray remains Mukse.
One exception to the rule of "Ba'sees" is when the Mukse was not placed on the base deliberately. For example, the money was left on the tray unintentionally; it was forgotten there, not in its usual place. In such a case, the tray does not become a "Ba'sees." Therefore, it is permissible to shake the tray until the money falls off, and then handle the tray freely. There is no problem removing the money indirectly by manipulating the tray. This is considered "Tiltul Min Ha'sad L'sorech Davar Ha'mutar"-indirect moving of Mukse with intent for the permitted item, namely, the tray.
The Rema clarifies that a person cannot render someone else's vessel a "Ba'sees," even if he deliberately placed the Mukse there. For example, if a Shabbat guest intentionally places his change on a tray that belongs to his host for safekeeping until after Shabbat, that tray does not become Mukse. The reason is "En Adam Oser Kelim Shel Havero"-One cannot prohibit someone else's utensils. The classic example of this principle is Avoda Zara-idol worship. If someone bows down to his friend's animal, the animal does not become forbidden. Of course, the money in the tray remains Mukse, but it now becomes permitted for anyone to shake the money off and use the tray.
The Poskim debate a case in which a person deliberately placed the Mukse item in a container and the Mukse was situated on top of another permitted item within the container. For example, a person placed his wallet inside his valet case, piling it on top of his watch. The question is whether the watch now becomes Mukse as a "Ba'sees." The Trumat Ha'deshen (Siman 193) is stringent. On the other hand, the Magen Abraham is lenient, arguing that the watch does not serve as the base of the wallet, it settled there only to conserve space. Hacham Ovadia (Vol. 3, p. 132) rules in accordance with the strict opinion. Accordingly, the watch becomes Mukse and may not be worn on Shabbat. Therefore, one should take care not to stow his Mukse items on top of other items he may need on Shabbat. A classic application of this Halacha is in the freezer. If a woman stuffed frozen raw fish, which is Mukse, into the freezer, finding a space for it on top of frozen food which is not Mukse, there is a question whether that food becomes Mukse as a Ba'sees. According to the Trumat Ha'deshen, it would become Mukse. However, there is a question whether food can become a Ba'sees or is this Halacha limited only to Kelim (Utensils).
SUMMARY
A non-Mukse item become a Ba'sees only if the Mukse was place on it intentionally and the non-Mukse item belongs to the person placing the Mukse item. A non-Mukse item can become a Ba'sees, even if it is not intrinsically serving the Mukse item resting on top of it.
