Recursive Filter on Nested array

You could reduce the array and build new objects with optional children, if they have a length not zero.

function filter(array, fn) {
    return array.reduce((r, o) => {
        var children = filter(o.children || [], fn);
        if (fn(o) || children.length) r.push(Object.assign({}, o, children.length && { children }));
        return r;
    }, []);
}

var data = [{ name: 'bob', type: 1, children: [{ name: 'bob', type: 2, children: [{ name: 'mike', type: 3, children: [{ name: 'bob', type: 7 }, { name: 'same', typ: 9 }] }] }, { name: 'mike', type: 2 }] }],
    result = filter(data, ({ name }) => name.toLowerCase() === 'bob');

console.log(result);
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