@Ash***
An invalidity pension can be paid by private organizations to which a person has contributed, whether through employment covered by a pension scheme separate from the government system, through private insurance, or through other arrangements.
For example, it may result from an accident caused by a third party rather than from an illness.
In any case, that is not the issue here. My pension does not come from the government, and I am entitled to receive it for life, period.
I have no intention of changing my country of tax residence, so the question of whether the pension would continue to be paid does not arise either.