Tenant moving out earlier and how to coordinate

[Kati Xi]

My tenant gave 2 month notice to move out. Per the lease, they need to pay rent until the end of the second month. Their new home closed earlier and they are going to move out sooner. Now the house will be vacant for a month before next tenant. So I plan to do some work on the house. I guess if I am using the time to do some work, they would want to clean the house and give me the key before that so they do not have to have responsibility. Are they still supposed to pay the rent for this month then? I wonder how this kind of situation is usually coordinated. I am not a mean person as I allowed them to break lease and give two month notice to move out early. At the same time. I do not want them to not paying the last month rent and leave me a financial burden to swallow. I am looking for a win win solution.