if a small proportion of software errors turn into software failures; is it necessary to make investments to eliminate software errors?
Depends on who you ask, a developer will say yes, a manager/bean counter will look at the cost the failure causes and compare it to the cost of fixing the error
Depends on if the investment to eliminate the errors would be better value than to suffer the software failures.
The issue is that software errors can be detected earlier than software failures, so they are much cheaper to fix.
(It is estimated that) there is a factor of 10 in the cost of finding problems at each stage of development.
Software errors detected by e.g. static analysis, early during coding, are so much cheaper than software failures during Testing, or customer deployment, that it is worth fixing 100s or 1000s of software errors, in order to avoid 1 software failure on a customer's machine.