Running is acting as an adverb, not modifying, but adding extra information to the verb came.
"He entered the room" is the way the sentence should read
There was an interesting silence in the room when the principle came in.
The commotion in the room came to a complete halt as the prince strode confidently into the room.
there was a phantom in my room when i came home late that night
The dog retreated in disarray as the car came by. The room was in disarray.
The sounds of mirth and laughter came from this very school room.
The mice were scampering to and fro until the cat came into the room.
She heard a high pitched shriek, but then realized it came from the movie playing in the living room.
The nurses came rushing into the room when they heard the man calling for help.
The painter was doing a huge project that would leave many speechless. ;)
"Well, all I know is that the entire payroll was still in the safe until YOU came into the room", he said, insinuatingly.
Yes, silent is an adjective. It is a form of the noun or verb silence.