The government is subsidizing kpop companies somewhat via funding for arts and entertainment (as essentially all governments in a position to invest in soft power do, of course).
I'm not aware of any military backing, though. Kpop stars occasionally perform at army concerts - South Korea is a country with mandatory service for all young men, so as you can imagine these are popular -, and while I assume these are paying gigs it's also infrequent enough that I doubt you can call it backing.
