Praise be to Allah the Lord of the Worlds.
It is permissible to give Zakat (Alms) to the person who can`t afford treatment costs. This is because in terms of custom and Sharia such a person is considered poor, so he/she is amongst the eight categories eligible to receive Zakat. In addition, jurists have defined the poor person as follows: "One who neither has money nor a source of income to cover his and his dependents` essential needs; such as food, lodging and clothing."
Consequently, in light of Sharia and custom, the patient who can`t afford treatment expenses is poor; thus, it is permissible to give him/her Zakat. And Allah The Almighty Knows Best.