Can "badly" used in this way?

Yes, the sentence is fine.

What's the meaning of the word? Can you supply more examples?

' Badly' here mean 'very'. It is of course usually used in unfortunate situations:

I want a new car badly, but I have no money.
He had to go to the bathroom badly.

wangqh2696122Things started to go badly wrong for the family after the husband lost his job.

" ...Badly wrong ...." sounds odd in American English. Perhaps "Things started to go terribly wrong after the husband lost his job".

dimsumexpress" ...Badly wrong .." sounds odd in American English.

Is that so? I didn't realise there were any differences. On Google News Search I find quite a few instances of "badly wrong" in American newspapers.

I am used to hearing and reading "things go terribly wrong..." But couldn't rememberthe last time I heard " badly wrong " spoken. If my understanding is wrong, I stand corrected. But I so know "terribly wrong" is very common in AmE.