In all honesty, if she is ACTUALLY depressed, then these aren't symptoms of "being lazy". They are symptoms of, you guessed it, DEPRESSION.
Personally speaking, if you're in a bout of more intense, deep depression, it is very difficult to drag yourself out of bed, especially if you have no job and have no school. Very difficult.
However, I can't tell from the OP if the girl is actually depressed or if she is using the term "I'm depressed" loosely.
I would tell her to give it a chance. You don't have the money to send her back so give it more time and if it doesn't work out, THEN you can start having a conversation about sending her back.