My Earphone Wire Broke inside Earbud

Much of that stuff is throwaway these days. You're probably a lot better off just buying a new set.

Absolutely. I listen to audiobooks during my commutes. I buy new earbuds about once every three months. I have tried no-name cheap ones, and expensive branded ones such as Sennheiser. I try to be gentle but the constant flexing of the wires makes a break somewhere eventually. The longest lasting ones so far (4 months and still going strong) are a supermarket own-brand pair, from Lidl, the German chain who are opening up to 100 stores in the USA in 2017. The little gauze grille has gone off one of them (I don't think it's still in my ear!) but the sound is as good as ever. No point in spending a lot of money. These ones were 4.99 UKP, about 6.50 USD.

/looks in centrox's ear/

I don't see anything.

What? Speak up, why don't you?

I don't want this to be an 'ewww' moment, but they are going to get waxy, if I can put it that way, and unless you want to get busy with alcohol and Q-tips, which might shorten their life anyway, you may as well just get some new ones at that point.

Some people take these off anyhow before first use, to make the sound clearer, which is supposed to make all the ear debris end up inside the bud, but if we treat them as disposable, who cares?