A nice similie to help understand this ‘stream of consciousness’ is that of a river. Every second the river is different, yet it is still flowing and recognisable as a river - so it all depends on your perspective. So you may ask - what is river? what is mind? Personally, I find it helps to think of the mind, not as a ‘thing’ but as a process. The whole aim of meditation is to slow the movement of the mind, even to the point of stopping all movement. This lack of agitating ‘process’ is stillness/peace. So rather than asking ‘when does the mind die’, one could reframe it to - when/how does the process of mind cease The answer is contained in the teachings on Dependent Origination/Liberation
The answer is contained in the teachings on Dependent Origination/Liberation