Typically, will government programs or insurance companies pay for out of country, way cheaper assisted living?

Government programs don't normally cover assisted living. The only exception I know is a few who are covered by Medicaid partially after a person runs out of money. Medicaid is administered by the states within the state, so wouldn't pay anywhere beyond their borders.

When it comes to LT insurance carriers, it would be in the policy. Facilities have to meet certain requirements for these policies to pay. The companies are numerous, so you would have to read the policy of the individual company and product purchased.