gistfile1.txt

    internal class A
    {
        public string uid { get; set; }
    }

    public static class Class1
    {
        public static void Run()
        {
            var regexp = new Regex(@"'uid':\s*(?<uid>[0-9]{8}[0-9]+)\s*", RegexOptions.Multiline);

            var value = @"
    {
    'uid': 200532601548057346057920392776 }";

            value = regexp.Replace(value, "'uid':'$1'");
            var a = JsonConvert.DeserializeObject<A>(value);
            Debug.Assert(a.uid == "200532601548057346057920392776");

            value = @"
    {
    'uid': 200532 }";

            value = regexp.Replace(value, "'uid':'$1'");

            a = JsonConvert.DeserializeObject<A>(value);
            Debug.Assert(a.uid == "200532");
        }
    }