Unravel = unfold, disentangle or untangle.
Idiomatically, gradually being dispensed, revealed or exposed.
"Falling apart" is not what it means.
If you choose "getting undone", it does not mean "falling apart" kind of "undone" but the "untangle" kind of undone.
Think of the issue as a huge mess of tangled up string, and someone (or some set of events) are attempting to unravel (straighten up) the string.
The result of disentangling could be starting to get a clearer picture of the situation, or could be starting to feel the effects of the situation.
The causes of the housing financial bubble began to unravel
= The causes of the housing financial bubble was gradually being revealed.
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The effects of the housing bubble began to unravel after years of accumulated malpractice
= The effects of the housing bubble started to roll out after years of accumulated malpractice.
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The years of intricate Japanese anti-competitive relationships between conglomerates were unraveling upon the economy of Japan in the 1990s, causing a lost generation of Japanese economic output.
= The years of intricate Japanese anti-competitive relationships between conglomerates were unfolding their effects upon the economy of Japan in the 1990s, causing a lost generation of Japanese economic output