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Sometimes a mistake, a wrongdoing or a lie becomes worse and when you try to correct the mistake, it becomes two new mistakes. And if you confront a lie, you might get two new lies.

In programming computers this happens when a technical problem becomes two new technical problems and so on.

I use my own expression "exploding error" which I must explain if I use it. Is there a common word? There is the expression "opposite effect", is that the best expression?

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    Apart from the snowball effect mentioned in other answers, there is chain reaction, which is perhaps a better match to your exploding error. – TonyK Dec 25 '16 at 16:23
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    Positive feedback or, more dramatically, runaway are common terms. Negative feedback is characteristic of functional systems; positive feedback can be heard by putting a microphone in front of its speaker. – John Lawler Dec 25 '16 at 21:31
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    "The error correction went from bad to worse and from worse to total disaster". – Graffito Dec 25 '16 at 22:16
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    In system design for fault tolerance, error propagation is to be avoided. The definition of exploding error is succinctly a (sub) system failure, meaning the effect could not be tolerated. – Fuhrmanator Dec 26 '16 at 20:00
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You could say the problems snowballed

to increase, accumulate, expand, or multiply at a rapidly accelerating rate

You might also invoke a comparison with the Hydra where

if you cut one hydra head, two more grow back

Other relevant terms might be "domino effect" and "cascading failure"

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    As a personal anecdote, my peers and I (at college) use "hydra bug" or just "hydra" when you fix a bug and it causes (or maybe just reveals!) others. – Fund Monica's Lawsuit Dec 26 '16 at 15:31
  • @QPaysTaxes I like that bug term. It's perfect to describe the common situation when "I tried to fix that bug. Now I got two problems..." – Niklas R. Dec 26 '16 at 23:45
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Two other terms come to mind:

Mushroom or mushrooming (verb): Increase, spread, or develop rapidly (https://en.oxforddictionaries.com/definition/mushroom)

Where one problem or error triggers another, and that triggers another, and so on, they are often referred to as cascading errors or problems.

(https://en.oxforddictionaries.com/definition/cascade):

A succession of devices or stages in a process, each of which triggers or initiates the next.

also related definition of the term:

A large number or amount of something occurring at the same time

But cascading isn't generally used in the sense of multiplying exponentially.

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I hear the term "snowball effect" the most, when people refer to compounded lies or problems. It is defined on Wikipedia as "Metaphorically, a snowball effect is a process that starts from an initial state of small significance and builds upon itself, becoming larger (graver, more serious), and also perhaps potentially dangerous or disastrous (a vicious circle, a "spiral of decline"), though it might be beneficial instead (a virtuous circle)."

I usually hear the term "opposite effect" when people mean "paradoxical reaction"; if you took medicine to lose weight but it made you gain more weight, that would be, not a "side effect" but, an "opposite effect". For your examples, using either the term "opposite effect" or "paradoxical reaction" could work if you're referring to the actions of confronting (the lie) or correcting (the technical problem) and receiving the opposite of that which the action intended. But in referring to the actual lies or technical problems themselves, those would be snowballs or exploding errors.

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A dramatic way of putting it would be to say that someone is caught in a web of lies.

For a much more dry, technical term, you might call this a cascading error, or say that an initial mistake was compounded by further attempts to conceal it.

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