Kyle. I agree with the resources shared here to guide the tenant storage process.
Assuming there will be no mutual agreement in writing to end the tenancy, the residential tenancy with an order granting the Landlord possession ends when 1) The sheriff serves the writ of recovery, then returns to remove the tenant or 2) the tenant "abandons" the unit during the eviction process and moves out. Yes, Minn. Stat. 504B.271 refers to "Tenant's Personal Property Remaining in Premises," but please note you will first need to comply with 504B.365 and specifically Subd. 3 Removal and Storage of Property. You will notice 504B.365 Subd. 3(d) is where the tie into Minn. Stat. 504B.271 appears. That is the link from the writ to the landlord storage regulation.
A few key pieces of 504B.365 Subd. 3(d): (When sheriff returns a 2nd time to move out the tenant--different from where the tenant "abandons" on his/her own prior to sheriff return move out)
-The landlord has specific personal property inventory and tenant inventory notice requirements.
-The landlord has phone and mail notice requirements to notify the tenant of date and time of the sheriff move out.
-Take photos of each and every room and additional photos of questionable items (TV is an old TV not a new flat screen, etc.). If you do a "photo" inventory with sheriff, I advise uploading the photos and emailing or texting a link or even mailing a cheap USB with the photos. Bad faith tenants are unlikely to pursue landlords for damages when they know any bluff will be called in short order.
If the tenant "abandons" the unit based upon facts (no notice in writing, but all non-trash personal property removed, utility changed billing, , etc.), I advise writing a "Notice of Abandonment" letter to the tenant that is mailed and emailed to last known address. This document effectively ends the tenancy under Minn. Stat. 504B.365 Subd. 3(g) and tells the tenant you the landlord now have lawful possession. Be very careful of bad faith tenants and "unlawful ouster" that arises in 504B.365 Subd. 5, 504B.231, and penalties in 504B.225 which include "reasonable attorney fees." In short, hesitate before you change the locks because you believe the tenant may not live there (half moved out). If you have an old lease authorizing attorney fees, and your tenant hooks up with the right contingency attorney, you could be out thousands if you act too fast.
Last comment. Once the tenant is out and you lawfully change the locks, you need to pay attention to 504B.271 Subd. 2. This statute authorizes punitive damages to the landlord if you do not provide access to personal property with 24 hours notice written notice (after you change the locks). The problem is a bad faith tenant may want to come and go multiple times for an hour at a time for several weeks. In that case, I advise landlords to error on the side of a lot of time for the first move out time and advise the tenant (in writing) to bring friends, rent a truck, and that you are not required to allow them multiple short times to access their personal property over and over again. There is a fine line here, but you get the idea. If a tenant asks for access to personal property, open the door and grant a full day to remove items (assuming not a threat to property damage). Then return to lock the property up. Make sure to check all windows are shut, closed, and locked after each access.
Practically, when you seek to turn the unit, do your best to move into one room or the garage (if garage water/weather tight and no electronics in cold winter) and clean the unit and re-rent. Yes, if you plan to re-rent and store on-site, you cannot remove those items during that 28 day period from the end of the tenancy. As @Dan Vleck stated, rent the house without the garage or retain storage rights in the basement, etc.
If you have a multi unit apartment building, I do not advise common area storage for the 28 days of personal property. Then you may have a theft issue. Leave the abandoned personal property in the unit or place into a locked room on site.
Good luck!