Verb + -ing form strings have various structures.
[A] as analysed by Collins
[From the CoBuild works:]
V -ing constructions:
The verb is followed by an '-ing' form.
This pattern has three structures:
Structure I: Verbs in phase (i.e. complex verb groups) She started walking.
Structure II: Verb with Object He liked dancing with her.
Structure III: Verb with Adjunct They ended up fighting.
There is also the even less cohesive structure, which uses the ing-form or participial construction as an adjunct:
He went, singing. / He went, singing at the top of his voice.
This is not the same structure as the phase structure
He went singing / shopping / dancing / bowling / fishing.
Sometimes, these strings are hard to analyse.
Under the trees, he stood watching the fight. [probably a phase structure]
Under the trees he stood, watching the fight. [definitely not catenative]
He left singing. [left the profession]
He left, singing. [he seemed happy as he left]