Ceilings on property sales prices are very rare. Probably the most common example is resale price caps on government sponsored housing for lower income buyers.
Price ceilings on rent are more common but still rare. This is commonly known as rent control.
Like all price caps the result is shortages in varying degrees depending on how binding the ceiling is. If the rent/price is set below operating/construction costs you will see very little avalabilty/construction. On the other hand if the ceiling is set well above the "natural" rent/price there will be little if any impact. In between you will see increasing shortages as the ceiling decreases.
This is generally basic economics but can get pretty complex depending on the details of the specific policy. Taking thsee details into account as well as the unusual nature or real estate (durability, immobility, etc.) the actual results have lined up very well with the theoretical predictions.