Are all dead plant cells (that die to do a job), have secondary wall?
Not all plant cells perform a function when they die.
But a lot do.
Sclerenchyma is refereed to as:

Sclerenchyma is the tissue which makes the plant hard and stiff...


Mature sclerenchyma is composed of dead cells with extremely thick cell walls (secondary walls).

Plant cell death includes necrosis, apoptosis and autophagy and studying how and why they occur is an active area of plant research.
Some plant cells die because they are not provided enough energy. Plants garner energy via the sun and biochemical process known as photosynthesis.
When the days start to become shorter there is less sunlight and parts of some plants die.
E.g. Leaves die.