Hmm. To me there seems to be a subtle difference between (1a) and (1b):

1a. She ran out of the room angry.
1b. She ran out of the room angrily.

Which may be paraphrased as in (2a) and (2b):

2a. She ran our of the room while she was angry.
2b. She ran out of the room in an angry manner.

Ceci n'est pas un seing.