The simplest recipe for writing "almost bug-free" software is:

  1.  Freeze the set of features.
  2.  Continue to pay programmers to polish the software for several years while it is being actively used by many people.
  3.  Resist adding new features or updating the software to feel modern.

Of course, your users will complain about missing features, how ugly and ancient your products look, and how they wished you were more like your buggy competitors.

And if your users are unhappy, then you probably lose the "used heavily by a lot of people" part that reveals the bugs.

There is no system without exploitable breaches, whether technical or social ones. The biggest point is, who have the incitives to exploit them, how much resources it costs to run a trial, how much resources do they control and are they ready to throw at attempts.