「fall apart」の使い方

It might be hard to tell what that is a photo of. It's my two-year-old cap. I've used it and washed it too many times, so now it's falling apart.

The definition for "fall apart" in this sentence from Eijiro on the Web is ボロボロになる. There are a lot of other meanings, like in my sentence below. Take a look at the other definitions of "fall apart":

http://eow.alc.co.jp/fall+apart/UTF-8/

The mesh is coming undone, and I'm afraid the whole back is close to unraveling.

• come undone ほどける、失敗する、破滅する (definition from Eijiro on the Web)
• unravel 【自動】解ける、ほどける、ほぐれる、明らかになる、ほころびる、解体｛かいたい｝する、分解｛ぶんかい｝する 【他動】～をほどく、ほぐす、～を解く、解明｛かいめい｝する、〔計画｛けいかく｝を〕つぶす (definition from Eijiro on the Web)

At least I have other caps to wear as backups to this one.

At the same time, it seems that Japan's old nuclear plans are falling apart. China's plan to sell high-speed rail to the rest of the world seems to be coming undone, too. The American economy is unraveling. I wonder what backups to use in these situations? Dark days, huh?

• dark days 失意の時代、不遇の時代 (definition from Eijiro on the Web)