Most of the conditions that caused economic hardship in North Korea were not caused by the deaths of the two leaders. Instead, these conditions have existed most of the time in North Korea due to its strictly communist economy.
As can be seen in the telegraph.co link below, famine can be a serious problem in North Korea at any time. This is due to the fact that the Kim dynasty has not allowed its economy to open up in any serious way. People are essentially not allowed any private property and cannot do anything like growing excess food to sell. Because the economy is centrally planned, it tends to have a lot of trouble producing enough to feed its people.
The basic condition that causes the economic hardship in North Korea, then, is its centrally planned communist economy.