The asset in question can be (and have been) not other than another currency paying a higher interest rate.
When asset prices decline (as has been the case in stocks, and commodities, etc), the loans that were made in Yen have to be paid back.
Therefore, now people need to buy yen. Since there have been an accumulation of position over a long period of time, the buyers of Yen all of sudden overcome the sellers of Yen. Supply and demand then dictates a higher price for Yen, and in a shorer period of time.
Once the trend is set, speculators use the trend to drive the price of Yen even higher.