You can still be made to work out your full month's notice even if you have holiday owing. You end up getting paid out any holiday pay owing.
Unpaid sick leave is really the same as unpaid leave. If your sick and run out of sick pay you dip into any annual leave owing, then after that it...
Because she handed in her notice, the company are entitled to tell her to take leave (if any is owing) as part of her 1 month's notice period.
The leave accrued whilst off sick would only apply to a period of paid sick leave, not unpaid sick leave.