... They had several tools for carving foam from blocks. One of those tools was a machine like a bandsaw which worked with a very thin wire. Using that they could slice through the foam and cut it into shapes....
This would be a hot-wire foam cutter. An electrical current runs through the wire making it hot, and it melts through the foam. It is very important to note that some foams smoke is toxic, and should not be cut with this method.
If you want to pursue this method there are many DYI plans out there on the Internet. But again, be careful what types of foam you cut and pay close attention to ventilation. Also be careful about the design as some I've seen are a definate shock hazard. I run mine through an isolation transformer and only cut polystyrene foam (the extruded rigid insulation foam) .... for my lost-foam casting patterns, not pool cue cases.
Dave