Right.
Within a phenomenological paradigm, ‘thought’ can and does stop. From a literal biological standpoint it only ‘seems’ to stop.
This is because a phenomenological perspective stresses the subjective perception rather than the objective process.
Similarly, if your task is to track surface-level topographical features, and you’re following a river, and the river becomes subterranean, then it is accurate to say that ‘the river disappears’ because we are not including sub-surface phenomena in our geographical account.
‘Thought’ is same. We, for reasons of tradition and common practice, categorize some sub-forms of neural/mental activity as ‘thought’ and other forms of neural/mental activity in other ways. We also define the boundaries of thought’s existence as formed by the limits of subjective awareness. So if mental activity goes outside of the bounds of awareness or occurs outside of those conventionally-defined forms of activity, we say that it has ‘stopped’. And that is okay.
From my perspective (because I do not subscribe to those conventions of categorizing mental activity), if your heart is beating in rhythm, then your autonomic nervous system is ‘thinking’.