Singapore is an interesting example of a country where they've mostly socialized housing to great success.
You can still buy property if you are very wealthy, but 80%+ of the population lives in a government (heavily) subsidized "HDB" - Housing Development Block - basically massive apartment blocks, that the government builds by the 10s of thousands. You then get a "99 year lease" to the property, though, by the time the property starts to get around 40-50 years old (HDBs have only been around that long) - the government will usually build much nicer, newer buildings, and give the occupants of the old building first right of refusal of (collectively) moving out of the old one and signing a new 99 year lease (Known as Selective Enbloc Redevelopment Scheme) - it remains to be seen if there will be any leases that ever expire.
As a result, property is affordable to all citizens, though if you are less well off, there is a good chance you will be living with other family members sharing rent - Singapore is a much more family oriented country, so this is normal and accepted. Also, if you are price sensitive, you might chose to live in a somewhat more distant property (known as New Estate, as compared to Mature Estate that has lots of shops, transit, built up around it).
And, then if you strike it rich - and don't like the HDB lifestyle, you can go buy a Condo (has lawn, pool, security, gym, usually nicer architecture) for 2x what a similar HDB would have cost you.
Singapore is a fabulously expensive country for expats to live in - but they've done a great job (amazing job) of keeping it very affordable for citizens. Transportation, Food, Housing, Healthcare Insurance - all of the essentials have had a lot of work put into them to keep everything cheap, cheap for the citizenry.