So Hendrik answer on my question
brought me back to the feared and famous Ablativus Absolutus (at least on my school mates). Wikipedia states that there are relics of it named as Genitivus Absolutus
stehenden Fußes, klopfenden Herzens...
But they are declared as stehende Ausdrücke. Means imho, you can use the known and only the known but are not allowed/animated to build new ones yourself like sinkenden Hauptes, which would be same grammatical structure as above examples.
In English it actually seems you are allowed to do this in form of the Nominative absolute with any noun and particple.
So is there a at most complete list of these german stehenden Ausdrücke you can use? Or maybe we can just put links/examples here in a cw? Im a true lover of the Genitiv and Ablativus Absolutus :)