Depends really on whether you have state run archaeology or free market lead.
In a major city archaeologists know what finds they will make before they dig, and companies are required by law to let them perform archaeology on the site before the dig takes place. They are allotted a time period to complete this during the construction. Occaisionally they make a surprise major find is made, such as the Rose theatre in London. If you have state run archaeology like most European countries, Italy, France so on. The goverment will purchase the site from the developer and preserve as a national monument. If you live in a free market lead archaeology country, UK, US, Holland, so on. The archaeologists dig the site the best they can in the alloted time, concrete the find over to preserve it and the building construction goes ahead.