Tanto en inglés como en español el participio puede tener su propio sujeto.

Ejemplo
All details being thought of, we started the project.
sujeto de la frase principal: we; sujeto del participio: all details
The city was full of tourist, some of the ladies being dressed very nicely.
sujeto de la frase principal: the city; sujeto del participio: some (of the ladies)
Tom was sitting in a park, with his lunch resting on his knees.
sujeto de la frase principal: Tom; sujeto del participio: his lunch