No, bacteria do not all eventually die. All bacteria alive today are descended from bacteria that DID NOT DIE - they split and live on in the form of at least one living ‘descendant’.
“The point is that if the cell dies, it was a stress. If it does not die, it wasn't a stress.” AndrewC
So how does a cell “know” it is under stress you ask? Apparently by your ludicrous definition - when it is DEAD it knows it was under stress!
A stress is something that interferes with the living processes of a cell. It can be an antibiotic, a toxin, heat, cold, high pressure, low pressure - anything that can be detected through molecular mechanisms that causes interference in the living processes of the cell.
These molecular mechanisms that detect cellular distress start a signaling transduction pathway that activates transcription factors that enable the expression of stress response genes.
One of these stress response genes is error prone DNA polymerase.
Why it is expressed during stress is because, as you helpfully point out - if it didn't change it would (be more likely to) die.
Now what is changing when error prone DNA polymerase is used during cellular reproduction instead of high fidelity DNA polymerase?
The entire genome, not just psuedogenes, not just things from your absurdly small “tote bag” - NO! The ENTIRE GENOME is subject to change - and good thing too - because during during extreme heat stress (for example) a large % of genes would need mutations that made them more stable at high temperatures in order to survive and thrive at higher and higher temperatures.
Okay, so now you see it as a definition problem. Clearly, my statement applies to the situation in which the cell does not respond or inadequately responds to the stress. Look at slide 22 of the pdf. It clearly shows the delay for MCS2. On the other hand, MCS1366 does not have the proper tool in the totebag(It was removed by the researcher) and it will die. A bacteria will not die if it gets a little more "food", but it does react.
The rest of our post establishes that a complex directed response is provoked prior too any increase in the use of error prone DNA polymerase.