Manifest grave sin means a serious, publicly known sin. This does not simply mean that the priest is aware of it. An example would be a politician who consistently supports abortion. Because of the public nature of his sin, he cannot receive sacraments like the Eucharist and Anointing of the Sick unless he repents.
If the person is unable to go to confession, e.g., if he is unconscious then he may be anointed even if he is in the state of sin where it is presumed that he would desire confession if it were possible. If it is possible, he must go to confession before being anointed.
If the person is in danger of death, any priest would be able to hear his confession.