Do blood sugar levels naturally go down for type ii diabetics when they sleep?

Not always: In the early morning hours you have what it is called the "dawn" phenomenom during which you secrete "stress" hormones that prepare you for waking up. These hormones bring sugar out of your liver, so you might actually find that your blood sugar waking up are higher that what you had at bedtime despite not having anything to eat.

No: If you're on Insulin or other oral hypoglycemic agents then you could have overnight low blood sugar. Occasionally someone might have a low blood sugar overnight but the natural direction of overnight-early morning blood sugar in an untreated type 2 diabetes patient is up. The liver makes glucose which isn't suppressed enough because of Insulin resistance.