Thanks for writing in.
Its possible that the black stuff in her vomit/sputum is blood and we need to address this as soon as possible. The other possibility is that of an aspergilloma
which is a fungal infection
. Its possible that the cancer which has spread to the lungs has eroded into a blood vessel which is now bleeding. This is not an indicator of the extent of the lung involvement. This could quickly lead to a deterioration in her health. Please see a physician and get this addressed.
Hope this helps