How can you have a can of soup without the can? So yes, the can is a subset of the can of soup. Of course one can say they had a can of soup for lunch but, that's merely figurative ... I hope.
Yeah,

is right! Iacchus, it appears that you do not understand the basic terminology and concepts of ninth-grade set theory, but I am running out of ways to try to explain it! I am running out of emphatic fonts here. Apparently a size 7 "NO" was not emphatic enough to convince you. Should I paint it red? How about
NO!
I'm sorry I cannot figure out a way to make it flash too.
You cannot have a can of soup without the can, but the fact that the can is a component of the assembly called "a can of soup" does not make the can a subset of the can of soup, and it certainly does not make the soup a subset of the can that contains it. A set is, by definition, an unordered grouping of objects which have some property in common. Please read that sentence again, so that you understand what a set is, and try also to understand the implication of the term "unordered."
The can could, of course, be a subset of the set of "things which are either cans or soup," but it is not a subset of the set of "cans of soup" because membership in that set, by definition, requires that any member of that set be a can of soup, and all subsets and members of those subsets must qualify as members of the set. An empty can is not a can of soup, so an empty can cannot be a member of the set of cans of soup. Membership in a set requires that the thing be one of the things defined as a part of the set! The set of cans of soup can contain only cans of soup as members, hence also can contain only smaller sets of cans of soup as its subsets.
Have I said that in enough different ways that it begins to penetrate? A single can of soup is a subset of the set of all cans of soup. That subset is a set with one member: itself. To suggest that an empty can is a subset of a can of soup is to require that the empty can be identical to a can of soup. This is not to suggest in any way that a can is not a requisite element in the assembly of a can of soup, but it is not a matter for set theory. It is not an issue of sets. Sets are not what you are talking about when you make that observation.
Similarly, you can treat numbers as the objects in a set. The numbers IN the set are not the same as the number of members in the set. The number 2 is a set by itself - the set of the number two, and it has a single member. It is also a subset of many other sets, the set of real numbers, the set of integers, the set of positive numbers, the set of even numbers, and so forth. However, as a set, the number two is a set with one member: itself; and consequently only one subset: itself! The fact that the number one can be doubled to add up to two does not make the number one a subset of the number two, and the fact that the set of the number two has one element does not make two a subset of one either. The fact that a set of two widgets contains as subsets two individual widgets still does not make the number one a subset of the number two, because a set of widgets is a set of widgets, not of numbers. Quite apart from the above, there is another rule of sets, which is that a set cannot contain multiple copies of the same thing. It can contain multiple objects that are functionally identical, such as the cigarettes in a pack, but these objects are distinct and individual. The cigarettes in the pack are not the same cigarette counted twenty times over. The number one cannot, therefore, be a subset of the number two, because there is only one number one. The number one is unique. To suggest that the number one is a subset of the number two would require that there be two of them in the set, but there can be only one, and unless 1=2, it cannot be.
Edit: I realize I made a mistake above when I said the single element set of the number two, the can, etc. has only one subset: itself. Actually, an single element set has two subsets, itself and the null set, which is the subset of all subsets. I don't think that makes a difference, but I figured I'd better catch that before someone else does.