By subsidize housing you mean that the government builds housing which they then sell to citizens. Which is a form of middle class welfare, but quite different from what most westerners would consider subsidized housing.
If you’re unemployed in Singapore, you get 3 months worth of welfare from the government. After that you rely on your own savings. (Unless you’re permanently disabled)
Going from first principles though, Singapore has a large ethnically Chinese population which tends to take care of family members / elders more than in the west.
Unless western countries are willing to adopt a culture of filial piety where you can live with your parents until you’re married and your parents expect you to take care of them in old age, I don’t see them replicating that feature.
If you’re unemployed in Singapore, you get 3 months worth of welfare from the government. After that you rely on your own savings. (Unless you’re permanently disabled)