A recent question on verb agreement left me one unresolved issue — can we add the verb leave to the list of verbs with copular uses?
The heat left me parched.
The shutdown left me out of a job.
The scandal left me boss.
The verb has a weak semantic value that contributes aspectual information, but little else. The same is true of turns out, remains, and stays. These all appear on copular verb lists.
Leave does not work in the common copular construction where a subject is matched to a complement that is usually a noun or adjective, but may sometimes be a number of other things.
Rather, it works as an object-focused copula (a label I found in only one document on the web, so I’m hoping for a more established term).
Examples of object-focused copulas include
Naming verbs — They made her the manager
Positioning verbs — She put it down
The first involves a noun phrase and the second an adverbial. What happened to object-focused adjective complements? Adjective complements are extremely common subject compliments.
Is "leave" an object-focused copula above? Is parched an adjective complement to the object?
CGEL‘s take on this is that leave is a complex-transitive verb with depictive predicative complement.
1. Predicative complements (PCs) and complex-transitive and complex-intransitive constructions
To begin with, here is how CGEL introduces the complex-intransitive and the complex transitive construction (in the same place where it introduces predicative complements):
 COMPLEX-INTRANSITIVE COMPLEX-TRANSITIVE
a. This seems a
idea/fair. b. I consider this a
good idea / fair.
S P PC S P Od PC
We use the term complex-intransitive for a clause containing a
predicative complement but no object, and complex-transitive for
one containing both types of complement.
The major syntactic difference between a predicative complement and an
object is that the former can be realised by an adjective, such as
fair in these examples. Semantically, an object characteristically refers to some participant in the situation but with a different
semantic role from the subject, whereas a predicative complement
characteristically denotes a property that is ascribed to the referent
of the subject (in a complex-intransitive)or object (in a
2. Copula vs. complex-intransitive construction
CGEL uses the term copula only for certain uses of the verb be. In a note on p. 218, CGEL says that
The term ‘copular’ is widely used for [5i] (Ed seemed quite
competent, [complex-intransitive: S-P-PCS]) and the like
as well as  (Ed was quite competent); we prefer to restrict it to
the latter, using ‘complex-intransitive’ for the more general
construction, partly to bring out the parallel between [5i] (Ed
seemed quite competent) and [5ii] (She considered Ed quite
competent [complex-transitive: S-P-O-PCO]), partly because
complex-intransitive verbs other than be are not mere syntactic
copulas but do express semantic predication.
In short, verbs other than be that other sources call copular CGEL prefers to label complex-intransitive verbs. And what your source calls ‘object-focused copulas’, CGEL would call ‘complex-transitive’.
3. The classification of the verb leave and similar complex-transitive verbs
Terminology aside, CGEL provides a classification of verbs taking predicative complements (pp. 263–266). The verb leave appears in ‘Class 3’ (pp. 264–265):
■ Class 3 verbs: complex-transitives with depictive PCs
 She believed it prudent/an advantage to be out of
town. We proved it genuine/a
fake. They kept their
marriage secret/a secret.
There are considerably more verbs in this class, and we therefore list
separately those with the ‘inf ‘ annotation indicating the possibility
of an infinitival complement instead of the PC: compare the believe
and prove examples in  with She believed it to be prudent to
stay out of town and We proved it to be genuine.
[The annotation ‘adj’ indicates that the PC is restricted, or
virtually restricted, to AdjPs to the exclusion of NPs.]
 i believe
adj inf judge
inf prove inf
ii account brand call designate1 esteem
adj hold2 imagine keep label
leave rate term wish
Hold1 means roughly "consider", as in I hold you responsible for her safety, while hold2 is close to
"keep", as in She held the door open for us; They held us hostage
(in both cases the range of PCs is quite limited). Some verbs in [ii]
do enter into the infinitival complement construction but without the
semantic equivalence that obtains in [i]. For example, He wished
himself different from the sort of person he thought he was is closer
to He wished that he were different than to He wished himself to be
different (which indicates wanting to change). He imagined himself
unmarried does have an interpretation equivalent to He imagined
himself to be unmarried (i.e. "He thought he was unmarried" – cf. He
imagined himself indispensable) but it also has another
interpretation, probably more salient, in which he knew he wasn’t
unmarried but imagined what it would be like if he were.
A few verbs not included above, such as acknowledge, confess,
suppose, appear in the complex-transitive construction, but normally
only with a reflexive object: He confessed himself puzzled by her
response, but not *He confessed the decision
For completeness, here is an abbreviate description of all five classes of verbs taking PCs:
Class 1 verbs: complex-intransitives with depictive PCs (this class includes be):
Kim felt lonely/an intruder. Her son remained ill/a danger. That seems plausible/a good idea. Pat proved reliable/a great asset.
Class 2 verbs: complex-intransitives with resultative PCs
He became ill/our main ally. The work got too difficult for them.
Class 3 verbs: complex-transitives with depictive PCs
She believed it prudent/an advantage to be out of town. We proved it genuine/a fake. They kept their marriage secret/a secret.
Class 4 verbs: complex-transitives with obligatory resultative PCs
They appointed her ambassador to Canada. You drive me mad. They made him anxious/ treasurer. They created her a life peer.
Class 5 verbs: complex-transitives with optional resultatives
We hammered it flat. Kim knocked him senseless. You should paint the house green. She rubbed herself dry. He pushed the door open. I’ll wipe it clean.
As Edwin Ashworth pointed out in the comments, it seems that leave really can be used in two senses, one depictive (which therefore belongs to Class 3), and one resultative, which arguably belongs to Class 4:
[A] i They left1 him sleeping/asleep on the couch. [depictive]
ii The crisis left2 him pennyless/a pauper. [resultative]
The authors of CGEL anticipated that some of these distinctions might have been left out of their classification (pp. 265–266):
The primarily semantic distinction between depictive and resultative
PCs is not always easy to draw. We have distinguished two senses of
designate with one taking a depictive ("officially classify", as in They have designated1 it a disaster area), and the other a resultative ("choose, appoint", as in They have designated2 Kim the
next Attorney-General), and it may be that some others should
likewise be dually classified. Compare, for example, We had half the
children sick (depictive) vs We had the meal ready in half an hour