In the long run, price ceilings such as rent control do not end up providing more low-cost housing in a given area. In this way, they are typically somewhat counterproductive.
The law of supply tells us that lower prices will result in a lower quantity supplied. Meanwhile, the law of demand tells us that lower prices will result in a higher quantity demanded. This means that a price ceiling will result in a shortage of a given commodity.
In the case of low-cost housing, price ceilings will make potential landlords shy away from owning apartments. They will try to convert their apartments into other sorts of spaces so they can avoid having their profits reduced. If they cannot move into a different line of business, they will try to do other things to avoid losing money. For example, they may skimp on maintenance, thus making the housing much less livable.
When governments impose price ceilings, they generally cause suppliers to try to get out of the market in question. For this reason, a price ceiling on housing is unlikely to lead to the creation of more housing.