EnumSet and EnumMap each have a

private static final Enum<?>[] ZERO_LENGTH_ENUM_ARRAY = new Enum<?>[0];

In EnumMap it's unused, but in EnumSet it's used for serialization purposes: 

    SerializationProxy(EnumSet<E> set) {
        elementType = set.elementType;
        elements = set.toArray(ZERO_LENGTH_ENUM_ARRAY);
    }

Having these constants is hardly justified[1] and incurs an ever so slight startup/footprint cost by loading Enum[].class

[1] http://shipilev.net/blog/2016/arrays-wisdom-ancients/#_caching_the_array