Can you put foam into closed cavity walls?

Yes. We have a product called "Pour-in-Place" foam that is ideal for existing structures where both the interior and exterior the walls are intact but have no insulation inside.  Also known as "frothing foam", this product is injected into the wall cavity via1/2" holes. The foam then rises very slowly like a cake rising in the oven, so that no pressure build up disturbs the existing walls.  The cured foam does not outgas, and forms a perfect air and vapor barrier, and of course makes for superior insulation too.