Temasek Holdings controls quite a substantial share in Singapore Airlines I think.
Between Changi Airport and Singapore Airlines, the government will prioritize Changi as seen from the liberal air policy.
But SQ is a national carrier and national pride, the Singapore government won't allow it to fail. If they have to bail out only one carrier, between SQ and Jetstar, they will bail out SQ. In times of crisis, they still need Singapore Airlines, see the thread on the government arranging for Singapore Airlines to bring Singapore students in the UK home.