We, as hobbyists dealing with this kind of part on a one-by-one basis, are not as much "exposed" as the OEM manufacturer who buys this crap by the case and loads it up into his board-stuffing machine. A prior, well-documented example of Taiwanese capacitors with faulty electrolyte (the formula stolen from another manufacturer...except it was a faulty formula) includes tales of many consumer and industrial products which used the bad capacitors. The example I am most familiar with is their use in a popular line of LCD computer monitors. A major technology firm serving clients in the oil industry re-equipped several of their facilities with these LCD monitors. This amounted to hundreds, perhaps over a thousand of them. Over time, about a third have failed and more are failing every day.
Where we can run across this, is when the excess production of parts gets surplussed or sold to retailers. For my parts, I often frequent a local store selling electronic surplus, and often run across bins of "no-name" parts of which I know nothing.