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.

Definitions of collapsible
  1. adjective
    capable of collapsing or being collapsed
    “a collapsible boat”
    synonyms: collapsable
    foldable, foldaway, folding
    capable of being folded up and stored
    having parts that slide one within another
    constructed so as to tip up or out of the way
Word Family

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