Of course it is possible. You should try to make sure she eats something. The elimination will come naturaly then. Is there a litter box in the room she is in now? or would she need to go to the basement? If you closed her in the bedroom, with the others outside, for just a while, would she freak out? If not, then I'd give her all the necessities in there for maybe a day and see what she does. Kind of testing to see if she'd eat or drink ond use the box (measure her food and water so you know for sure) Of course you could just take her back to her room down stairs and see if she comes back up.
Let us know what you try