Subscription implies a service that is paid for on a regular basis. Membership may be paid for, but that is not implied.
I could be a member of the Zooey Deschanel fan club for free, but subscribe to the monthly Zooey Deschanel magazine for $20 a year, for example. A man can dream...
Also, one can be described as a member of organisations that actually pay you, like the armed forces or emergency services.
Members of a subscription system are generally referred to as subscribers, but this is context sensitive. Your friend could simply refer to them as customers, as that's the usual word for someone paying for goods or services.
Segments
Some objects are naturally segmented, they have marks or narrowings between segments. These are places where the object can be easily and naturally separated. The segments are usually all alike in form. Think of an orange.
Parts
Some objects are compound objects that consist of an assembly of smaller dissimilar objects. We can separate these compound objects these into their constituent parts. Think of an internal combustion engine.
Pieces
Some objects don't have obvious segments but can still be divided into pieces at arbitrary points. The pieces need not be even in size and there is an undertone of destructive or irreversible breaking. Think of a (stereotypical circular uniform) cake.
Fragments
Some objects, when subjected to some sufficiently violent force, can shatter into multiple fragments of mostly random size and shape. If the other fragments are lost, you may find only one fragment and have no other knowledge of the form of the whole object. Think of a dropped Ming vase.
Sections
Some objects are designed to be cut apart or are commonly cut apart. The word section is derived from the Latin word for cutting and may be appropriate for a deliberate and careful cutting of some extract from a larger source. There is, to me, an implication that the cutting points are not accidental. Think of plumbing pipes
English text
Written English language text is usually written in sentences, paragraphs and perhaps chapters. These form obvious segmentation points, so when your extract is made at a balanced pair of such boundaries, the term segment is more appropriate. However, why not just use sentence or paragraph as appropriate?
If you spilled ink onto a page of text, it might be better to say that a part of the text was obscured - since (unless by unlikely coincidence) the obscured part is not an exact sentence or paragraph.
If a page of text is burnt or torn and scattered, you might consider any remainder to be a fragment.
As HorusKul commented, since successive English sentences are not often very similar, they are not very much like segments and the word section is more likely to be appropriate.
Updated to clarify segments, pieces, parts and sections. Updated: fragments.
Best Answer
There is a broad overlap between sign and symbol; it's a nuanced distinction.
In your examples, sign should be read as a synonym for evidence. More broadly, there is an intrinsic link between the sign and what it signifies. On the other hand, a symbol is merely a declaration that has an imposed relationship with what it declares.
For example, one might say that a smile is a sign of contentment if it is accepted that contented people tend to smile. One could also say that a smile is a symbol of contentment, but that would be a relationship between a smile and the concept of contentment (an imposed relationship - concepts don't smile), not between a smile and a contented person (an intrinsic relationship).
If, in a hypothetical culture, bananas were placed in front of contented people, one might say that a banana is a symbol of contentment, but it would be weird to say that a banana is a sign of contentment because there is no intrinsic link between contentment and bananas (contentment doesn't produce bananas).
So in your first example, I'd call meat with hair a symbol unless you read a mystical component into the context. The bananas in your second example are definitely symbols - they represent a wish and are not a by-product (or herald) of happiness.