Regarding
The Joy of Not Being Married
First, keep in mind that lots of books have titles like "The Joy of _" -- it is something of an idiom (from The Joy of Sex to The Joy of X (a book about math)...). Like most book titles, these titles aren't complete sentences: they're just stating the subject of the book, which in this case is "What Makes [Subject] Great."
The form is "The Joy of [word or phrase that functions as a noun]". So you have books like "The Joy of Cooking", where "cooking" is (as you know) a gerund (an action considered as an object, so it acts as a noun grammatically), or "The Joy of Not Working", which is about the positive aspects of retirement.
In English, "marrying" refers to the actual act of getting married. So instead the author uses "being married", where "married" by itself is a participle, a verb form that acts as an adjective. Put it together and "being married" means "the state of having a spouse" and acts as a noun. With "not," it's a book about how it's awesome to be not-married. Maybe why it's great to be single, maybe why it's great to be recently divorced, etc.
Regarding
The Joy of Not Being Sold Anything
Again, this is a variation of the stock phrase. It would also help to point out that "being sold [a thing]" has the connotation of "being subject to someone's sales pitch" or "having someone try to sell you something." (See sell definition 4). So the ad is really just saying "Isn't it nice not to have to listen to a sales pitch here? Now please buy our product."
All this discussion aside, to actually answer the question you asked: you are correct that this is a sentence fragment. That's why "to be" is absent. (As opposed to what you might be used to seeing in full sentences, something like "He is being sold a donut.")
SENTENCE 1:
He is afraid of being hated.
You have to learn how the adjective - afraid - is used in a sentence. What it licenses etc. A good place to look for those things is a good learners' dictionary. Look here.
You see there?
- afraid of doing something - I started to feel afraid of going out alone at night.
So the adjective - afraid - licenses a Preposition Phrase (PP) - of doing something - headed by the head preposition - of. Inside the PP, the head preposition - of - take a Gerund-Participle form of verb - doing something - as a complement.
Now that you know about the usage of the adjective - afraid, consider the following sentence -
He is afraid of feeding his dogs.
He is afraid is fine. Now, what he fears? This is to be introduced by a PP headed by a preposition - of. Here he is to feed the dogs and he fears to perform that action. So feeding the dogs is what he fears. This Gerund-Participle form of verb - feeding the dogs - will be the complement of the preposition - of - inside the PP.
Now concentrate on your sentence -
He is afraid is fine. What he fears? that people will hate him. We can't use hating him as a complement of of inside the PP. Why? Because then it would mean that the action - hating - to be performed by the subject of the sentence - he. But that is not the intended meaning. So we have to look for other alternatives. What he fears? (he is) to be hated (by people) is what he fears. That gives the intended meaning. So of being hated can act as a complement of the adjective - afraid.
He is afraid of being hated.
SENTENCE 2:
I remember being taken to Delhi as a small boy.
I guess you don't have any problem with the part as a small boy, so for simplicity I remove that part.
I remember being taken to Delhi.
So what I said earlier? Learn the usage of words. Here the verb - remember. This will help.
- remember doing something Do you remember switching the lights off before we came out?
What you remember? switching the lights off Who is performing the action of switching the lights off? The subject - you - itself.
But in your sentence it's a bit different. The action of taking to Delhi is not being performed by the subject - I. But by some other person.
What do I remember? (I am) being taken to Delhi (by some one) is what I remember. So it's
I remember being taken to Delhi.
Hope I could help. You can ask in comments if you need any more clarification.
Best Answer
Yes, it is a grammatically correct sentence in the Present Progressive tense. It uses the Passive Voice too.
It says that someone is actively missing you (wishes you were near them), but says nothing about who exactly is missing you.
Transforming it into the Active Voice, we may get the following sentence:
What can vary is the part in the brackets: it depends on who exactly is missing the person. It can me [I am], [she is], [he is], [they are] etc.
The word missed is not in the Past Tense in your example. It is in the Past Participle form. It has been put into this form to help form the Passive Voice construction, which consists of the verb to be + Past Participle.
Your sentence without the Progressive aspect will look like this:
Then we add being to form the Progressive Aspect, in order to highlight the fact that the process of missing you is actively happening right now, that someone is actively missing you at this moment: