What is the meaning of using a past participle after 'of'?

Prepositions and -ing forms:

Many prepositions take noun phrases as Complements, for example the preposition of:

• I'm scared of spiders.

In the sentence above, we see the noun phrase spiders occurring as the Complement of the preposition. When we want to use a verb (technically a clause) as the Complement of a preposition like of, we need to use an -ing form of the verb ( a gerund-participle):

• I'm scared of flying.

So here we see the -ing form of the verb fly occurring after the preposition of.

The fact above leads many teachers and grammar books to tell readers that:

• 1. We need to use an -ing form of the verb after a preposition.

Of course, this rule is not clear enough. I mentioned above that in sentences like these we should really think about the bit after the preposition as being a clause not just a verb. If we give the verb an overt Subject, this will be clearer:

• I'm tired of Bob getting all the best jobs.

Here we see the clause Bob getting all the best jobs occurring after the preposition of. Notice that this is a clause headed by the ing form of the verb GET. So in this example, the verb getting is not occurring after the preposition. What we see is a clause after the preposition of, and this clause must use an -ing form of the verb.

So, maybe we need to reformulate this rule. Perhaps we could say:

• 2. When we want to use a clause after a preposition, we need to use a clause headed by an -ing form.

Assuming that we are talking just about prepositions which usually take noun phrases as Complements, is the rule above ok? The answer is no! The rule in (2) is missing the important word Complement (some grammars use the term Object). Just because a verb or clause appears after a preposition, it does not mean that that verb/clause is the Complement of the preposition. Consider the following example:

• The spider you are scared of died.

In the sentence above, we see the verb died occurring after the preposition of. However, this verb is not the Complement of the preposition. The word of is part of a relative clause. This relative clause is part of the Subject. We can model the sentence like this:

• [The spider (that) you are scared of] died.

In the model above we can see that the Subject consists of a noun phrase the spider modified by a relative clause (that) you are scared of. The word that is optional here. So, if died is not the Complement of the preposition of, what exactly is the Complement of this preposition? The answer is that the Complement of the preposition is a gap. We understand the gap to refer to the spider. We can model the sentence like this:

• The spider that [you are scared of him] died.
• The spider_(i) that [you are scared of ___(i)] died.

In the sentence above, the verb died is the verb in the main clause. It is not the Complement of the preposition of and therefore it does not need to be an -ing form of the verb. We need to reformulate our rule like this:

• 3. When we want to use a clause as the Complement of a preposition, we need to use a clause headed by an -ing form.

The Original Poster's example

Now some character he'd never heard of had underbid and outperformed him.

We can remove the word now here, it is not important for the grammar of the sentence. This give us:

• Some character he'd never heard of had underbid and outperformed him.

This sentence has a relative clause where the word that (or whom) has been omitted. If we take out the relative clause, the sentence looks like this:

• Some character had underbid and outperformed him.

In the sentence above we can see that the verb phrase uses a past perfect construction had underbid and outperformed. The past perfect is just used to show that the underbidding and outperforming happened before the time we are thinking about. The past perfect construction is just part of the normal tense usage within the sentence.

The preposition of in the example, has a gap as a Complement. This gap refers to some character:

• Some character [he'd never heard of that character] had underbid and outperformed him.

This relative clause is part of the Subject of the larger sentence— in bold above. We can see from the example that even though the verb phrase "had underbid and outperformed ..." occurs directly after the preposition of, it is not a Complement of that preposition. Because of this, we do not need to use an -ing form of the verb. The fact that the verb uses a past perfect construction is unrelated to the preposition. It's just the normal use of verb forms within the larger sentence.

It is correct. But if the sentence were better punctuated you would understand more clearly what has happened.

Had I written it, I would have put parenthetical commas around he'd never heard of.

In other words the of is not operating in conjunction with the verb which follows, but forms part of the previous clause.

Some might argue that it should have said: of whom he'd never heard, and they could be regarded as having a point. Some of the more literate class in Britain, would have said that. And it would have been better English, in my view.

But since it is perfectly idiomatic to put prepositions at the ends of phrases, and most people do it every day, the sentence should be regarded as correct as it stands. But the punctuation is lacking.