Is there such a thing as a catch-all key for a javascript object?

You're looking for __noSuchMethod__:
JavaScript getter for all properties

You can create a JavaScript object with 'wildcard' or 'catch-all' keys using a Proxy and a getter function. Unlike the solutions provided, a Proxy should work in just about any environment, including Node.js

var foo = new Object()

var specialFoo = new Proxy(foo, {
    get(target,name) {
        // do something here
        return name
    }
})

console.log(specialFoo.blabla) // this will output "blabla"

If you want the properties to be callable, simply return a function:

var specialFoo = new Proxy(foo, {
    get(target,name) {
        return function() {
            console.log('derp')
            return name
        }
    }
})


specialFoo.callMe() // this will print derp

Details: documentation on mozilla