Is there a name for letting something get worse until it is so bad it has to be addressed properly?
Solution 1:
It may pertain to the maxim "the worse, the better", often attributed to Vladimir Lenin in the years before the Communist Revolution.
There is a related philosophical idea: the modern (Hegelian/Marxist) use of the term dialectic. Hegel's idea was that each concept or position, theoretical as well as practical, continues to develope until it becomes useless and corrupt - entangled in its own contradictions. Then, a shift is made to another concept/position - the negation of the previous concept/position. Marx used the same idea in economical and political contexts. Hence the famous prediction concerning the imminent collapse of capitalistic economies, destined to be caught up in their own contradictions, until there is no remedy but a popular workers revolution.
Solution 2:
As a British English speaker, I would use the rather broad but appropriate phrase of..
"come to a head"
If something comes to a head or someone brings something to a head, a situation reaches a point where something must be done about it.
Solution 3:
The best I can come up with right now is fester
Oxford examples use the word in context both of politics and relationships:
(Of a negative feeling or a problem) become worse or more intense, especially through long-term neglect or indifference:
Without freedom of the press, such problems will only fester, and that is not in the long-term interest of the United States.
The threat may ultimately have less to do with competitive fire than with a readiness to let resentments fester and anger flare without feeling any need to bridle emotions or discipline his temper.
Admittedly, this term doesn't quite guarantee the 'it has to be addressed properly' part.
I'll keep thinking.
Solution 4:
You can allow for something to escalate.
escalate verb
make or become more intense or serious
The disturbance escalated into a full-scale riot.
Source: Oxford Dictionaries Online
An example:
The problem escalated so much that it had to be dealt with instantly.
Solution 5:
People often talk about 'hitting rock bottom' to describe the situation you're talking about.
You might talk about an addict hitting rock bottom before they were motivated to improve their life. An organization might have to hit rock bottom before they're compelled to adjust their management structure.
I feel like there might be a better term for this but it's not coming to me.