In another question, I asked for the grammaticality of:
Senkenden Hauptes schlief sie langsam ein.
which may be a possible, uncommon abbreviation of
Während sie das Haupt senkte, schlief sie langsam ein.
Here, I am asking what other 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?