Although Samsung (NASDAQOTH:SSNLF) remains the world's largest smartphone vendor, the South Korean tech giant has certainly seen better days: Rising competition from China, coupled with a more competitive high-end landscape, has taken a toll on the company's profits. With the introduction of Apple's (NASDAQ:AAPL) iPhone 6 Plus, Samsung faces intense competition in the one niche (large-screen phones) it previously dominated.

But the company might be poised for a sharp rebound. Next year, Samsung could introduce a radical new smartphone, one far different than any other handset that has come before it.

Flexing and bending
Samsung plans to launch a smartphone with a flexible display -- so flexible, in fact, that users will be able to fold it in half.

Samsung has released smartphones with nontraditional displays before: Its first curved smartphone, the Galaxy Round, debuted in 2013, and the Galaxy Note Edge -- a phablet with a curved, edge display -- went on sale earlier this month. But some have written these devices off as mere gimmicks, and perhaps for good reason -- the utility gained by a slightly curved phone or curved screen is debatable at best.

In contrast, the appeal of a foldable smartphone is obvious. The most salient, long-standing criticism of large-screen smartphones has been the difficulty in carrying them around -- it's simply a challenge to fit them in all but the largest pockets. Last month, China Unicom, one of China's largest mobile phone carriers, ran a promotion that offered free tailoring services to iPhone 6 Plus buyers looking to have their pockets enlarged. Although it might have been more of a marketing stunt than anything else, it certainly drove home the point.

Apple could struggle to match this
If Samsung can introduce a foldable smartphone, it would have a huge advantage (at least temporarily) over its competitors, notably Apple.

Samsung has been a longtime supporter of OLED display technology, which it has used in nearly every Galaxy smartphone. OLED is not without its drawbacks, but it does offer a tremendous advantage: it can flex. Apple, in contrast, has long stuck by LCD. Compared to OLED, LCD offers more accurate colors and lesser power consumption in certain situations, but it can't be made to flex (at least not easily).

Samsung's management insists it will have an advantage in foldable smartphones, with its display subsidiary able to produce 30,000-40,000 flexible smartphone displays per month by 2016.

Don't count out Samsung yet
But even 40,000 a month is less than half a million a year, and given that Samsung has been selling about 300 million smartphones annually, its foldable phone -- when it appears -- could remain a high-end niche offering for quite some time. Still, it could give Samsung a smartphone that would set it apart from the competition, and if it can ramp up production fast enough, the company could repeat the success it had with its early, large-screen Notes that faced little competition their first few years on the market.

The decline in Samsung's profits has taken a toll on its stock -- the company currently trades at a stunningly low price-to-earnings ratio near six. Investors may be betting that Samsung will follow the unfortunate path of once-dominant handset makers HTC, Nokia, and BlackBerry. Ultimately, that could be the case -- but if it can continue to offer innovative, unique hardware, its mobile business could persevere.

Sam Mattera has no position in any stocks mentioned. The Motley Fool recommends Apple. The Motley Fool owns shares of Apple. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.