In Singapore, a government agency called the Housing and Development Board (HDB) builds housing (mostly apartment buildings). HDB is not meant to be profitable. It loses money every year and is subsidized from the government budget.
HDB ensures that its buildings have access all the standard infrastructure nearby - mass transit, retail stores, schools, medical and recreational facilities, etc before tenants move in.
HDB also ensures that the tenant population is diverse and no ethnic group is disproportionally overrepresented in any location (i.e. they will reject a prospective tenant in a location belonging to an ethnic group that they already have too much of).
About 80% of the Singapore population lives in HDB apartments.
The tenants have an option to sign a 99-year lease. About 90% of the tenants choose this option. They're not quite "owners" (the government is the owner and the landlord), but close enough with the 99-year lease - they can re-sell the apartment, hopefully at a profit. The remaining ~10% tenants rent short-term, usually because they can't afford the 99-year lease.
The government has a Central Provident Fund (CPF). CPF withhold 37% of everyone's income into 3 accounts: retirement (like U.S. Social Security), medical care, and housing. for most people, the money accumulated in their CPF account is enough to cover downpayment and most of mortgage payments. Singapore citizens (but not permanent residents) receive certain government-funded subsidies when buying the 99-year leases.
This Wikipedia page has more details and history.