For someone with larynx cancer 4th stage, can it be cured?

Unfortunately No: Stage IV cancer, by definition has spread to other organs and cannot be cured.

Stage IV: Contrary to other cancers, stage IV head and neck tumors are not always spread. Stage iva means a very advanced but localized cancer, stage ivb has lots of neck nodes, and stage ivc means distant spread. The last one would be considered incurable while the other 2 have a fighting chance (although i would say the odds are not great). If this is about you or a loved one, best to you.

Depends how stage 4: Laryngeal cancer can be stage 4 in a few different ways. If it is stage 4 because of being locally advanced, or because it involves lymph nodes--then, there is a chance. If it is stage 4 because it has spread to the lungs, then it is extremely unlikely that it will be cured. Even when it has spread to the lungs, it doesn't mean that there is nothing we can do, however.