The adjective afraid
The adjective afraid can take finite content clauses as complements. Normally afraid takes an of-preposition phrase if the speaker wants to explain what they are afraid of:
- I am afraid [of spiders]
- I am afraid [of people with beards]
However, the preposition of cannot take finite clauses as complements:
- *I am afraid of we will be late. [ungrammatical]
When we express what we are afraid of in a finite clause, the clause appears as a complement of the adjective, appearing directly after it:
- I am afraid we will be late.
We can optionally use the word that to introduce the clause:
- I am afraid that we'll be late.
This is what we see in the Original Poster's example, where the finite clause (that) she's gone too far this time expresses what the speaker fears.
Relative clauses after adjectives
Relative clauses can be used to modify adjectives and adjective phrases:
- She was afraid, which I didn't want her to be.
Notice however, that when a relative clause modifies an adjective, the relative clause must be introduced by which and preceded by a comma. Notice as well, that the relative clause does not explain what she was afraid of.
Content clauses versus relative clauses
Content clauses and relative clauses often look very similar. They often both allow for an optional that at the beginning. And they often appear in positions where it's difficult to tell them apart, for example when they occur after nouns:
- The idea (that) the government had proposed was ridiculous.
- The idea (that) the government had failed was ridiculous.
The first sentence here, containing a relative clause, has a gap after the verb proposed where the object of the verb is missing. We understand it to refer to the idea in question:
- The idea [the government had proposed
this idea] was ridiculous.
There is no such gap after failed because the second sentence does not contain a relative clause. Instead the clause after the word that tells us about the nature of the idea.
However, it is often difficult to see this kind of difference quickly or easily. A straightforward rule-of-thumb test is to replace that with the relative word which. If the sentence is grammatical the clause is a relative clause. If it isn't (or it radically changes the meaning), it's a content clause:
- The idea which the government had proposed was ridiculous.
- *The idea which the government had failed was ridiculous. (ungrammatical)
- *I am afraid which she has gone too far this time. (ungrammatical)
An analysis of the sentence
First of all, we need to distinguish grammatical relations like Subject, Complement and Modifier with categories of words and phrase like noun or noun phrase (notice that Subjects can be noun phrases, but do not need to be, and that noun phrases can be Subjects, but can do many other jobs as well).
The sentence can be split into a grammatical Subject, I and a grammatical Predicate (a)m afraid she's gone too far this time.
The Predicate consists of a verb phrase headed by the copula BE and a Predicative Complement (describing the Subject), an adjective phrase headed by the adjective afraid:
- afraid she's gone too far this time
This adjective phrase consists as we have said of the Head afraid and it's Complement, the content clause she's gone too far this time.
Analysis of the smaller content clause
The Subject is she, the Predicate, the verb phrase (ha)s gone too far this time.
The verb gone is taking a Locative Complement too far. The verb phrase has a Temporal Adjunct, this time, within which this is a determinative in Determiner function and time is a noun heading the noun phrase this time.