One example of an ore deposit that runs under a city is the banded iron formation ore in Kiruna. In this case the ore has been mined outside of the city since the turn of the previous century. The ore has been found to run under the city and there are now plans to move the city more detailed information. This has led to a process where the city has to be re-established in a different location including moving a large number of historically significant buildings.
A similar situation is also present in Malmberget (about 120 km S of Kiruna), part of the twin town of Gällivare-Malmberget. In this case the plan is to have Malmberget inhabitants to move to Gällivare. The mining activities at Malmberget have resulted in several collapse features see images on this link. There is also some information in English on the Gällivare web-site.
In both cases there are significant restructuring of the societies. It is also worth noting that the definition of ore is economical which means that what is worth mining depends on market prices. In the case of Iron the market has been strong but has fluctuated significantly. The result is that the planning and decisions for a move such as these are difficult since they are costly and depend on the market to be financially viable (it is the mining company that largely pays for the move).