If your husband is an heir/devisee you can't 'remove' his name from previously filed papers -- he was an interested party and will remain that under Michigan law.
If the house was not properly transferred from the estate, it will be in a legal 'grey area' until the taxes are unpaid long enough to cause a tax sale. If your husband truly doesn't want ANYTHING you don't need to to DO anything so long as his name was not put on any assets. You probably SHOULD be concerned enough to look into things though -- what attorney was handling the estate? A phone call may be in order.
If you aren't sure what has happened I would strongly urge you to consult with your own attorney however, and have that attorney contact the personal representative's counsel to determine what the status is and what is going on.
You probably don't need to 'worry' about anything, but the small fee to hire someone local to look into the matter will be well worth it for your peace of mind!
This answer is offered for informational purposes only and does not constitute legal advice or create an attorney/client relationship. I am licensed to practice in Michigan only. Please seek competent local legal help if you feel you need legal advice!
I respectfully disagree with my colleague. You are not forever stuck as an interested party, if you do not wish to be. Your husband can disclaim his share of the estate, at which point he ceases to be an interested party. Or, given that the estate is going to administratively close, if nothing else is done, he can allow the estate to administratively close. At that point, nothing can legally be done with any of the assets. I agree with Attorney Zichi that, once that happens, if payment is not made for taxes, the property will eventually be lost.
Your husband has no personal liability to pay any estate administrative expenses, merely because he is listed as a beneficiary. You will not be able to have your husband's name removed from paperwork that has already been filed with the court.
Your husband *could* hire an attorney to prepare the disclaimer, but I would imagine that is something he might be able to find a form for that would accomplish his objective. Since he is not interested in preserving any potential rights, the actual verbiage is somewhat less critical.
*** LEGAL DISCLAIMER I am licensed to practice law in the State of Michigan and have offices in Wayne and Ingham Counties. My practice is focused in the areas of estate planning and probate administration. I am ethically required to state that the above answer does not create an attorney/client relationship. These responses should be considered general legal education and are intended to provide general information about the question asked. Frequently, the question does not include important facts that, if known, could significantly change the answer. Information provided on this site should not be used as a substitute for competent legal advice from a licensed attorney that practices in your state. The law changes frequently and varies from state to state. If I refer to your state's laws, you should not rely on what I say; I just did a quick Internet search and found something that looked relevant that I hoped you would find helpful. You should verify and confirm any information provided with an attorney licensed in your state.