You are describing word association football, a variation on the classic rhetorical device anadiplosis, “the repetition of the last word (or phrase) from the previous line, clause, or sentence at the beginning of the next”.1 In this variation, anadiplosis is combined with ellipsis, “omission of a word or short phrase easily understood in context”.2
Word association football is essentially surprising in a humorous and literary sort of way, like a pun. Your examples are typical.
While not necessarily the originators of this rhetorical device, Monty Python get widespread credit for naming it.4 The name stems from one of their monologues.
Here is an example of anadiplosis, followed by the canonical example of word association football. Bolding, italics, and line breaks are added to emphasize the rhetorical structure.
Glad You Came (example of anadiplosis)
Turn the lights out now
Now, I'll take you by the hand
Hand you another drink
Drink it if you can
Can you spend a little time
Time is slipping away
Away from us, so stay
Stay with me I can make
Make you glad you came
—The Wanted3
Word Association Football
Tonight’s the night
I shall be talking about of flu
the subject of word association football.
This is a technique out a living
much used in the practice makes perfect
of psychoanalysister and brother
and one that has occupied piper
the majority rule
of my attention squad by the right number one two three
four the last five years to the memory.
It is quite remarkable baker charlie
how much the miller’s son
this so-called while you were out
word association immigrants’ problems
influences the manner from heaven
in which we sleekit cowering timrous beasties all-American
speak, the famous explorer.
And the really well that is
surprising partner in crime
is that a lot and his wife
of the lions’ feeding
time we may be c d e
effectively quite unaware of the fact or fiction section of the Watford Public Library
that we are even doing it is a far, far better thing that I do now then, now then, what's going Onward Christian Barnard the famous hearty part of the lettuce now praise famous mental homes for loonies like me.
So on the button,
my contention causing all the headaches,
is that unless we take into account of Monte Cristo
in our thinking George the Fifth
this phenomenon the other hand
we shall not be able satisfactor fiction section of the Watford Public Library again
ily to understand to attention when I’m talking to you and stop laughing
about human nature, man’s psychological make-up some story the wife’ll believe
and hence the very meaning of life itselfish bastard, I’ll kick him in the balls Pond Road.
—Monty Python
There are several possible descriptive terms for this rhetorical device. The most appropriate seems to be:
chiasmus
a reversal in the order of words in two otherwise parallel phrases, as
“flowers are lovely, love is flowerlike” (Coleridge). — chiastic, adj.
what is broken is made whole again,
what is soiled is again made clean.
The others are:
epanados
- the repeating of a phrase or sentence in reverse order.
what is broken is made whole again,
what is soiled is again made clean.
anastrophe
a rhetorical device in which the usual word order of a phrase or
sentence is reversed.
But what exactly is a rhetorical device? According to Wikipedia:
In rhetoric, a rhetorical device or resource of language is a
technique that an author or speaker uses to convey to the listener or reader a meaning with the goal of persuading him or her
towards considering a topic from a different perspective, using
sentences designed to encourage or provoke a rational argument from an
emotional display of a given perspective or action. Note that although
rhetorical devices may be used to evoke an emotional response in the
audience, this is not their primary purpose.
Emphasis mine
As a celebrated statesman of the 20th century, Dag Hammarskjöld demonstrated astute oratory and writing skills by choosing words, building phrases and designing sentences in a logical framework that appealed to the powerful pathos and ethos of his audience. He would have made a sufficient impact if he had simply applied the rhetorical device of metaphor:
Forgiveness is the answer to the child's dream of a miracle by which
what is broken is made whole again.
Regardless of the word order, he applied the literal terms broken and whole to the relational dynamic of forgiveness. He could have increased the impact of that statement by simply adding a second metaphor with the rhetorical devices of repetition and parallelism:
Forgiveness is the answer to the child's dream of a miracle by which
what is broken is made whole again,
what is soiled is made clean again.
His repetition device can be further classified into three separate repetition devices: Anaphora, Epistrophe, and Mesodiplosis. Apparently, he wished to multiply the impact of his statement with the specific emphasis of a fourth rhetorical device of chiasmus:
Forgiveness is the answer to the child's dream of a miracle by which
what is broken is made whole again,
what is soiled is again made clean.
Accomplished authors, like Dag Hammarskjöld, choose to employ the flexibility of English semantics and syntax to make an intentional logical and emotional impact on their audiences, who often enjoy the impact without ever recognizing the author's devices. We enjoy discovering and discussing their techniques with relish.
Best Answer
There is a device that often appears in Hebrew writings known as chiastic structure. Essentially it extends chiasmus (a common literary device that relates clauses in criss-cross fashion—think "the first shall be last and the last shall be first") to an entire passage. It is particularly common in Old Testament writing. Another word used to mean chiastic structure is palistrophe.
For example, a palistrophe or chiastic structure may have the form ABCDEDCBA, meaning that an idea A is presented, followed by an idea B, and so on. Thus the first idea presented is also the last. Other chiastic structures are possible, but they are still structured so that the first and last ideas are the same (or, at the very least, similar).
I think chiastic structure appropriately describes what you are seeking.
Added: a link to a picture of the chiastic structure of Genesis 6–9 for reference.