In addition to the answer by ChrisW, the following sutta quotes provide further perspective on the same topic.
From SN 22.93:
At Savatthi. “Bhikkhus, suppose there was a mountain river sweeping
downwards, flowing into the distance with a swift current. If on
either bank of the river kasa grass or kusa grass were to grow, it
would overhang it; if rushes, ...
No, they don't.
Those who claim a 'self' defined what they mean by the 'self' and some thinker at the time of Buddha, for example, the Sankhya philosophers posit a self that can not be annihilated and the Buddist show that it is not true.
It's like if group A says a unicorn exists. The Buddhist didn't say 'for a unicorn to exist it has to have a single horn ...
A sutta possibly providing an answer is the 2nd and most important sermon of the Buddha, namely, the Anatta-Lakkhana Sutta: The Discourse on the Not-self Characteristic. Relevant paragraphs for consideration are:
"...if form were self, then form would not
lead to affliction (ābādhāya) and it should obtain regarding form: 'May my form
be thus, may my ...
There is a line expressing that the notion of an annihilation of an existent self/being is a misrepresentation of the teacher's message.
It can be wrongly deducted that it therefore follows that the teacher's message is that an existent self couldn't be annihilated.
There is no Buddhist collective with a set of beliefs as it is not a homogeneous group.
Perhaps this is what you are remembering:
The Fruits of the Ascetic Life
3.3. The Doctrine of Ajita Kesakambala One time, sir, I approached Ajita Kesakambala and exchanged greetings with him. When the greetings
and polite conversation were over, I sat down to one side, and asked
him the same question.
He said: ‘Great king, there is no meaning in giving, ...
The first and perhaps most famous sutta like that which comes to mind is the Anatta-lakkhana Sutta: The Discourse on the Not-self Characteristic (SN22.59) translated here and here.
I think that says that if something (e.g. form or consciousness or feeling or perception) is impermanent, then it's "not fit" to be regarded as "self".