Millisatoshi (msat), or 0.001 of a satoshi, is already the base unit on the Lightning Network. For one millisatoshi to equal one US cent, then one bitcoin would have to equal one billion dollars, which would give bitcoin (assuming all 21 million had been mined) a marketcap of 21 quadrillion dollars.
What happens when BTC is worth $10 million ? 
Those crazy price predictions will only happen if dollar is affected by a very high inflation. It would not be bitcoin increasing its value, but dollar losing it. At this point, some other pair would be used against BTC, some other fiat or even gold (?)