As a self-contained solution in functional style, you can encode with:

plain.split("")
     .map(c => c.charCodeAt(0).toString(16).padStart(2, "0"))
     .join("");

The split on an empty string produces an array with one character (or rather, one UTF-16 codepoint) in each element. Then we can map each to a HEX string of the character code.

Then to decode:

hex.split(/(\w\w)/g)
   .filter(p => !!p)
   .map(c => String.fromCharCode(parseInt(c, 16)))
   .join("")

This time the regex passed to split captures groups of two characters, but this form of split will intersperse them with empty strings (the stuff "between" the captured groups, which is nothing!). So filter is used to remove the empty strings. Then map decodes each character.

Remember that a JavaScript code unit is 16 bits wide. Therefore the hex string form will be 4 digits per code unit.

usage:

var str = "\u6f22\u5b57"; // "\u6f22\u5b57" === "漢字"
alert(str.hexEncode().hexDecode());

String to hex form:

String.prototype.hexEncode = function(){
    var hex, i;

    var result = "";
    for (i=0; i<this.length; i++) {
        hex = this.charCodeAt(i).toString(16);
        result += ("000"+hex).slice(-4);
    }

    return result
}

Back again:

String.prototype.hexDecode = function(){
    var j;
    var hexes = this.match(/.{1,4}/g) || [];
    var back = "";
    for(j = 0; j<hexes.length; j++) {
        back += String.fromCharCode(parseInt(hexes[j], 16));
    }

    return back;
}