About This Answer
Does the knowing, or mindfulness, completely cease when an arahant dies? The answer, given through the interpreter, is that what ceases for an arahant is the defilements (kilesas), not the knowing nature of the mind.
For unenlightened beings and at every level of attainment, from stream-enterer through once-returner and non-returner, there is a knowing nature, often called "that which knows". In an arahant this knowing is pure, with no kilesa in it. At the arahant's death this purity, often called the Dhamma element, the basic pure knowing of the mind, moves to a spiritual sphere exclusive to purified minds.
Doubts and speculation on such a subject never end for the unenlightened. Those who truly want to know must bring their own minds to arahantship and see for themselves.