Something that can be folded down into a manageable size is said to be collapsible, i.e., able to be collapsed. It is used as an adjective, as in "He folded up the collapsible table and put it in his car."
Collapsible is formed from the verb collapse, which comes from the Latin collāpsus, "fallen together." This makes sense, since something that is collapsible "falls" into a tighter, more compact size or shape. Of course, anything that is able to fall can be considered collapsible, but the word refers more to something that is intentionally made to fall, rather than something like a rickety building that might collapse.