In pushing back against President-elect Donald J. Trump’s plan, President Xiomara Castro threatened that a base hosting U.S. troops could “lose all reason to exist in Honduras.”
Honduras, like many poor Central American countries, relies heavily on income from citizens living abroad. About 20% of its income comes from Hondurans living in the US.
One thing unmentioned, and I don't think this totally makes up for it but it's worth considering, is people stationed on the base will spend a lot of their pay in the local area. The areas around military bases can make a lot of money from military personnel, even if they aren't being paid directly.