I'm not expert, and indeed I would like to know the answer to your question. I would suggest that it lies in the reward system...
Motivation is the expectation of future reward. If there is a malfunction either in this predictive mechanism or in the valuation of reward then it could lead to the type of state you are pointing...
I agree Stephane. Although the word 'reward' has some unfortunate attributions. While also not an expert, I am aware that sometimes the 'normal' trend of interest leading to engagement can be reversed. ie engagement (in a task, activity etc) can lead to interest. In general, people need to be engaged in something worthwhile. So a strategy could be to require people to undertake meaningful tasks such as volunteer work with needy families, hospital visits to children etc. How one 'requires' people to engage in these tasks if they are resistant, I have no answer for.
I agree with the reward system to an extent, but I'm also aware that it requires a great deal of the person own willingness to change his/her situation and gathering this willingness might be the first battle to win.