An ordinary sale generally leaves the existing lease in place, and the buyer takes the property subject to the remaining lease term. Selling does not by itself make the tenant move. If you want the tenancy to end, the lease and applicable notice rules determine the next step; the sale alone does not set a move-out date.
The Michigan Judicial Institute explains how a new owner affects an existing tenancy in its Residential Landlord-Tenant Law Benchbook. Michigan's tenancy-termination notice statute is another source for the notice rules that may apply.
A sale also does not automatically release you from responsibility for the security deposit. One way Michigan law allows a seller to end that responsibility is to give the deposit to the new owner and notify the tenant by ordinary mail of the transfer and the new owner's name and address. Give the buyer the lease, deposit records, and tenant notices so the handoff can be handled at closing. See MCL 554.614 and the Michigan Legislature's practical guide for tenants and landlords.