Money invested from abroad is money coming inside the economy - whether the person lives there or not. That money goes to the seller, who'll then get taxed on it, spend it somewhere else... Or that money could be used, as I said, to build new buildings and rehabilitate old ones, thus creating jobs in the process. If the system was well set up for it, foreigners investing in a country is usually a good thing. The US is super foreign-investment friendly for example, doesn't hurt them.
Besides, if foreigners are investing solely to speculate - if they did fix the supply constraints, the opportunity for speculation would greatly decrease. It's only an attractive investment because the supply is so finite.