If I understand your question correctly, your landlord served you with a demand of possession after you have failed to pay for rent because of some issues that the landlord has failed to address in your apartment. If that is true, you will have to move, or the landlord will get an order to have you removed.
The "eviction letter," as you call it is properly known as a Notice to Quit. In most circumstances, the notice to quit is for failure to pay rent. When this occurs, you usually have a time period to pay your rent and you can continue to stay. However, if you landlord opts out of the complaint for failure to pay rent, and decides to get an order for possession, it means that it doesn't matter if you pay rent, you are out. The landlord can still go after you for failure to pay your rent.
You might say that you shouldn't have to pay rent for things that were wrong with the home. This is true - to an extent. You are always obligated to pay your rent, if you have a situation where the landlord won't fix a problem, you need to usually write the landlord so they have proper notice of the problem. If they then don't fix the problem, you can put your rent into an escrow account to force them to get the problem fixed. You can also hire someone to fix the issue and take that money off the rent (but only if the landlord refused to fix the problem).
From what your question is stating, you don't have much to go on, and will likely need to move.
Please review the Michigan Landlord Tenant Rights Handbook available on the State of Michigan's website... This identifies the PROCEDURE the landlord must use to evict you..
If they do not follow the procedure and simply set your belongings out in 48 hours they can be liable for $200 per DAY they interfered with your rights.
I highly reccomend you consult with a knowledgable attorney immediately
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