A sewing needle is classified as a "Keli She'm'lachto L'isur"-a utensil whose primary purpose is a prohibited function, namely sewing. It may be handled only "L'sorech M'komo," to make room for something else, or "L'sorech Gufo," for a permitted function, such as removing splinters. However, if the eye of the needle broke, whether before or on Shabbat, Maran rules that it becomes Mukse altogether and may not be moved for any purpose whatsoever, even though it is still useable to remove splinters. Since most people would now discard such a broken item, it becomes Mukse, even before it is discarded.
Some authorities, like Rav Shlomo Zalman Auerbach (Jerusalem, 1910-1995) apply this principle to disposable tableware that has already been used. They argue that since they are, by definition, destined to be thrown away, they become Mukse and may not be handled, unless there is still food in them or they become putrid.
Rav Pinhas Sheinberg (Jerusalem, 1910-2012) argues to be lenient and distinguishes between this case and the case of the needle. While true the disposable utensils are destined to be thrown away, they never broke and still retain their original form, whereas the needle broke. Moreover, the reason it is being thrown away is not because it is rejected; there is nothing inherently wrong with it. It is just so inexpensive that it doesnt pay to reuse it, as opposed to the needle, which is thrown away because it is faulty.
According to Hacham Yishak Beracha, the practical Halacha is that it is good to be stringent, but those who are lenient have upon what to rely. According to the strict opinion, if someone drank a cup of coffee in a disposable cup and then left it on the table, it may not subsequently be picked up and thrown out. The best thing to do is to either throw it away before putting it down or to leave a little bit of liquid inside. Otherwise, someone may unwittingly come and throw it out, not realizing that it is Halachic question.
SUMMARY
It is preferable to treat used disposable tableware as Mukse, but one may rely on the lenient opinions.
