The always interesting Jun Okumura at Globaltalk 21 has an interesting post about the (mis)use of "urban" and "rural" as terms for a very different dichotomy, between densely populated growth areas with much of the political, cultural and economic power on one hand; and stagnating regions on the other. I'm not going to wade into the terminology issue here, since I have no solution to that. Just try give a good term for places like Tokyo, Nagoya, Osaka and perhaps Sapporo on one hand; and Aomori, Miyazaki or the infamous Yubari on the other, and do so without building their differing economic and population trends into the definition. It's not so easy.
Anyway, Okumura asks towards the end what, if anything, can reverse the trend in many regions of stagnation and population decline. I suspect that for some places at least there is no stopping the decline. A flawed but quick assessment of a community would be to ask "If there was no village, town or city here today already, would anybody come here and create it?" Places don't spring into existence without reason, and in the long run they don't continue to exist if their reasons to do so are gone.
Perhaps one of the best, most drastic examples in Japan is Hashima island (also called "Gunkajima" - Battleship island - due to its silhouette on the sea). It was a thriving island city built around a productive coal mine. But once the mine was closed in the 1970's, it was quickly abandoned. There was simply no reason left to stay any longer. Today Gunkajima is an amazing place - a densely urban area left to naturally fall apart without human intervention. If you want to know what a modern industrialized city will look like when abandoned, all you have to do is take a look at some of the excellent photography from the place. Annoyingly there is not much high-quality footage posted online; Yuji Saiga has some stunning images, but marred by huge, annoying watermarks that make them almost unwatchable. A search through Google Images gives you another taste. The island is off limits to casual visitors (it's pretty dangerous), but there are occasional tours to small parts of it.
It's sad to say, but a fair number of places in Japan (and elsewhere) is undergoing the exact same process as Hashima island, but over the span of decades and centuries rather than months and years. Most settlements begin for some specific reason: it's a natural harbour; site of a mine, forest or other natural resource; or a river or train transport hub, perhaps. Or they're a company town, with one or two major employers driving the economy. But few reasons remain indefinitely. Mines become depleted, companies move or go bankrupt, transport shifts from rivers to train to roads (and upstream sources of goods may dwindle). Forestry, fishing and farming may be more stable, but they've seen amazing increases in productivity and efficiency. You need far fewer people to work in those fields (sic) than you did a generation or two back; there may simply not be enough farm or forestry workers left in an area to sustain the community that once grew around them.
If a community has reasons to exist independent of the original ones they may be fine. But if they haven't been able to diversify (such as the famous former mining town of Yubari), there just might not be a way to save the place. It's not that people move out - they do, but people move out of all places all the time. It's that without a reason for the town there is no reason for people to move back in any more. That leaves you a population that is dwindling, ageing and becoming less well trained and educated on average over time. that of course just accelerates the pace of change and makes it more difficult to reverse.
Some regional areas will be just fine. But some will not, and in the end there is no policy that will be able to prevent it. The best course in those cases may be to alleviate the hardship for the people affected and make the transition as painless as possible.