If someone broke their eyeglasses on Shabbat, are the broken glasses considered muktzeh?
This question needs to be divided into two separate parts. 1. The glasses themselves, and 2. The piece that broke off from the glasses — usually the eyepiece.
Regarding the glasses, the Shulchan Aruch says in סימן ש''ח סעיף ט"ז, we are not allowed to move a stove or bench with a missing leg, because we are concerned that someone might fix the stove by replacing the missing leg. That would be construction on Shabbat. Nevertheless, there are a few leniencies in this area:
If the missing leg broke, we are not concerned that someone may try to replace the leg, because it is broken, and therefore it is permissible for him to move the stove or bench.
If a person sat on this bench before Shabbat, we are not concerned they will fix the missing leg because they proved they can use the bench without the missing leg. Therefore, they can move the bench on Shabbat.
The מגן אברהם says that if the legs are connected to the bench loosely and not tightly, they are allowed to put the missing leg back.
If the leg is missing, the bench can’t be fixed. Therefore, one is allowed to move the bench.
Based on this halacha, just like the stove or bench that is missing a leg, the glasses would be considered muktzeh because there is a concern that one might reattach the eyepiece with screws. If the eyepiece is missing or broke, the glasses are not muktzeh because there is no way fix them on Shabbat. We can also say that even if the eyepiece is not missing or broken, since many people wear glasses with a broken eyepiece for a short period of time, there is no concern that someone might fix the glasses on Shabbat because they can still wear them. That is why we. hold that it is not muktzeh.
After all of this, I saw that this topic is debated between הרב משה פיינשטיין and הרב אורבך. According to הרב אורבך, eyeglasses missing the eyepiece and benches or stoves that are missing a leg are all inconvenient to use, and we are worried the someone might fix them. Therefore, we declare them muktzeh to use. However, הרב משה פיינשטיין holds that it is not the same. Many people wear eyeglasses with a missing eyepiece, so the glasses are not muktzeh.
In my opinion, it depends upon the person. There are some people that will never wear glasses with a missing eyepiece, and this type of person may fix the glasses. Whereas, there are other people who don't mind wearing glasses with a missing eyepiece, and don’t feel the need to fix the glasses. For them there is no concern (see Mishnah Berurah סימן ש''ח סעיף ז). Perhaps we can all agree that if someone wore the glasses with a missing eyepiece all week, there is no concern they may fix it on Shabbat, just as we learned regarding the bench.
Now regarding the eyepiece of the glasses, the Shulchan Aruch says in סימן ש"ח סעיף ח' that all keilim (which includes any container such as a wardrobe closet or a pot) may be moved on Shabbat, and that their covers (that is, a door for a wardrobe or a lid for a pot) that detached from the keilim may also be moved, whether the cover detached on a weekday or on Shabbat.
Based upon this halacha, you are allowed to move the eyepiece, even though it is not considered a vessel itself, but combined with the other parts the eyeglasses, the eyepiece is like the cover of a keilim and therefore not muktzeh.