1. She went shopping.
2. She came running towards me.
Whether the ing-form of the verb is a gerund or a participle is clear to me.
I know that these are not objects of the verbs 'go' and 'come', so they may be participle.
If they are participle then they must modify some noun or pronoun and the only pronoun in these sentences are 'she'.
Could you please explain it?