The rule in plain English
Michigan's deadlines run from the end of the tenant's occupancy. The tenant sends a forwarding address within 4 days. Within 30 days, the landlord mails a notice of damages with an itemized list and the balance of the deposit. Within 45 days, a landlord holding on to disputed damages files in court (MCL 554.609, 554.611, 554.613).
Missing the 30 days settles the question: no notice means no damages are due, and the whole deposit is owed (MCL 554.610).
For a tenant who is behind on rent, the Michigan notice is available here.
Prepare the Michigan noticeMore for Michigan landlords: Michigan Eviction Notice Selector · Eviction Notice Deadline Calculator · See the Michigan documents