Can we say that all plant cells that die to do a job (they are dead now), like the outer cell surface of the root cap, have secondary cell 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.
I add an answer since Andrew's answer "Do all plant cells that die do it while fullfiling a function" and the question asks wheater all plants cells that die to fulfill a function have a secondary wall. Hyper-virulence response is a plant defence mechanism from pathogenes similar to "scortched earth" strategy. The plant kills all cells near the infection to prevent the proliferation of the pathogen. If you consider this as a "job" than no, not all cells that fall in the line of duty have secondary walls