On Takkats advice i separated this part from this question:
"Senkenden Hauptes schlief sie langsam ein" - is this grammatically correct?
A (maybe) possible (but nowadays uncommon) abbreviation of
Während sie das Haupt senkte, schlief sie langsam ein.
The anwers here should focus on and explain what options one has in German to abbreviate a subordinate clause by use of participle structures. Maybe you give out a terminus for the grammatical structure and a short example?