OK - now it's clear. Always give a contextualised example - it saves misunderstanding.
Here the participle (it makes no difference whether one or two, or present or past participle) forms a non-finite subordinate clause. Non-finite means that the verbs have no stated subject in the subordinate clause. This can only be done when the subject is the same in both the main and subordinate clauses. It's the same as saying
Holmes lay curled upon the sofa. He was reading and re reading a letter... but the
He was is omitted and just "understood".
Here are some more examples :
He walked down the street, humming a song to himself.
Invented in the 1930s, pencillin has probably saved more lives than any other drug.
While living in Finland, I had several opportunities to see the Northern Lights.
Looking up and seeing me, he smiled.
In each case, the subject of the non-finite verb(s) in the subordinate clause is the same as the subject of the main clause. When it's not, then the sentence becomes ungrammatical - eg :
*
Turning the corner, the building came into sight.
Here the subject of "turning" is not "the building" and therefore the sentence makes no grammatical sense. It's what is known as a "dangling participle". You would need to say
As we turned the corner, the building came into sight to make the different subject explicit.
If you'd like further examples, this topic has already been dealt with here :
I don't know what to title this one