Earlier this month the L.A. Times reported on a new invention: a shopping cart which can convert to a small shelter for a homeless person. The mobile shelter is called an EDAR (short for Everyone Deserves a Roof) and was developed as the result of a competition sponsored by movie producer Peter Samuelson.
As you might suspect, a number of objections have been raised to this and similar undertakings. Don't want homeless people to get too comfortable, or they might have no incentive to seek more permanent solutions. (So meanwhile, it's OK for them to be subjected to rain and snow?) And where would you put them, seeing as there is no "unowned" land left anymore?
About 60 EDARs have been produced so far for a cost of a little under $500. The manufacturing cost could come down if a government or agency decided they'd be a good solution for temporary housing in a war or natural disaster.
Here's a website and video about the EDAR.