It is wonderful. When characters that you didn't see coming arrive then it's a wonder all its own. Stephen King, in his book, On Writing, A memoir of the craft said that it would happen, and that characters would do things you don't expect. I thought that was hogwash until it happened in my work. Then it was freaking awesome!
This type of inspiration also happens in non-fiction work. I have had an idea to write about, but it ended up going somewhere I never expected. Tonight I was working on Honor Battle and I wrote a couple characters in, or should I say a couple characters showed up. I'm laughing and getting excited as I watched what was happening in front of me. If you don't write fiction you won't get it and it will sound like garbage.
The author writes what he sees. I was writing this laughing, and I clapped because I was so happy to see these guys. If you read the book you'll know.
You're writing a scene and you're not always sure what's going on because it's foggy. The picture isn't clear. You mess with the antenna (dated myself) trying to get the picture right. Slowly but surely it clears up and you see what's happening.
Then you write what you see. As the story unfolds you transcribe it as quickly as you can because things are happening so fast.
I love writing the most for these moments, and they can't be forced. When it happens don't try to change anything. Just go with it. When you rewrite and if you hate them take it out. When the muse is there you need to go. Don't turn the muse away. She can stay away awhile if you reject her enough. OK, I'm really not that Pollyanna about the muse. I do think she's real. The muse responds to work and curse words. Truly believe that.