Rambo doubt it will over the next, nor actually ever.
Up to a certain size of public housing and depending on the family annual income, there are enough subsides and grants given out by the government to those who apply for flats. For e.g., a new 2 bedroom public house of about 50-60 sqm will coat between 50 to 150k SGD. However, There are several grants being put in place where the buyer can receive from 20 to 80k in grants. A singaporean who buys this house will either have enough in his Central Provident Funding account to pay off the remainder amount or to pay in installements. In short, no one (local) will be left “homeless” by the government, however, flats that do not meet the subsidy requirements (large size, near to city centre, and of course private apartments— their prices are on the rise for the past decade and may continue to do so)
For a foreigner to purchase an apartment in Singapore, It’s an entirely different matter as they cannot buy public housing.