My husband has a toe nail that is rotten & black & the nail is coming off, what could be the cause?

Most likely Fungus. This sounds like a fungal infection of the toenail. There are various treatment options. Topicals don't work well, but may if you are aggressive with treatment. Oral medication may be needed. This conditiion may be caused by repetitive trauma. Have him see your local podiatrist for evaluation and treatment options. Dr l.
Fungus infection. It sounds like a fungus infection. Have a doctor make the diagnosis.
Toenail. If he is an avid runner we see this often due to the recurring trauma.He may also have a fungal infection. He should be evaluated to make sure it is not an internal issue as well.