@Laundrysauce
Logistically, politically and socially, Japan can survive pretty long without outside support. Japan already boasts a 21% recycling rate in 2012 with a steady annual increase in recycling volume and efficiency. We know at least one Japanese village has zero trash and achieved 100% recycling rate last year.
Socially and cyulturally, the Japanese do not really need anything from the outside world. The Japanese exports culture and entertainment and do not really need entertainment as imports. The Japanese people are also quite xenophobic, and do not get depressed if they can't go to foreign countries. They don't need tourists from other countries either and couldn't care less about other countries's opinion of them.
The only problems would be food and raw materials. Japan is a geologically poor country, requiring massive amounts of resources to be brought in to support its industry. It also is not self-sufficient in food production, at least at their current level of consumption. Rationing will only last them so far, that's why food support from qua toyne is crucial.