Waking a sleeping Cohen when there is a dead body in his room

Is there an obligation to wake a sleeping Cohen when a person has passed away in his room, or since he is sleeping and considered as if he were legally incapable, and there is no need to wake him?

There is a commandment for anyone who knows that he is a Cohen to wake him in a case of biblical impurity, such as being in the same tent as a deceased person. However, in a case of rabbinic impurity, such as when the windows and doors are closed and the impurity has no way of leaving the room, there is no need to wake him.

The Remo wrote in section Yoreh Deah, chapter 372, paragraph 1, in the name of the Responsa of the Maharil, 'If a Cohen is sleeping, and a dead body is with him in the tent, they need to wake him and tell him so that he leaves.'
And the Shach wrote there in subsection 3, 'They need to wake him and tell him. For even without delay, the Cohen has transgressed, and even though he did not know, he has nonetheless committed a prohibition inadvertently. And even though he did not perform a prohibited act, there is a prohibition, and for others who know, there is a commandment to distance him from it.’ Thus wrote the Responsa of the Maharil, section 69: ‘Even though the Cohen isn’t actively doing it, and one is not flogged for a prohibition that does not involve an act, there is nonetheless a biblical prohibition.’ This implies that in case of a rabbinic prohibition, there is no need to wake him. And if so, where he is not in the tent with the deceased itself, but only in the house adjacent to it, if there is only a [rabbinic] prohibition, there is no need to wake him. And perhaps for this reason, the author was precise and wrote, 'and a deceased person is with him in the tent, they need to wake him.'