A bit of nomenclature may be helpful here. In some grammars, a (clause) has a subject and a predicate, the latter containing the verb and adjuncts not modifying the components of the subject. Your examples contain one clause apiece, call it a main or independent clause if you wish:
(She felt her eyes creak open as consciousness seeped into her), producing a soft gasp from her tired lungs.
(She stumbled back in horror), shielding her crying child.
(She leaned in close), her face [being] as kind as ever.
Each part outside the parens contains a present participle, but no subject. And none of them directly modifies either the subject or predicate of its associated main clause, but is associated with the entire thing. For instance, in the first example, producing a soft gasp partly describes the woman in question like a noun modifier, partly describes when the woman's eyes opened like a temporal adverbial modifier, and partly tells how she came into consciousness like an adverbial modifier of manner. In fact, the participial construct stands independent of the grammar of the main clause. Thus it is called an absolute construction, or a nominate absolute, in recognition of its association with the subject of the clause.
Applying the same analysis to the other examples, shielding and the elided being, is left as an exercise for the interested reader.
Notice that you can make the modifications explicit by rewording the sentences with dependent clauses:
1a. The woman who produced a soft gasp felt her eyes creak open.
(subject is modified)
1b. She felt her eyes creak open as she produced a soft gasp.
(verb is modified)
Or you can replace the absolute with a conjoined independent clause:
1c. She felt her eyes creak open, and she then produced a soft
But all these the options are grammatical, making the judgments of good, bad, and better a matter of style.