These people move here without credit so I presume they are putting up a lot of cash to buy the homes they live in.

In case you haven’t noticed, they give home loans to ANYONE including illegal aliens. Basically, if you are a living mammal some crooked mortgage broker will probably loan you the money for a $600K home. This is stopping now but it has been the case for the last few years. Foreign money is keeping the home market afloat, just not in the way you think. Foreign money buys a lot of doo-doo loans packaged into MBS. Without buyers for these garbage loans the whole house of cards collapses.