What should one do who is unable to fast due to psychological illnesses (such as chronic depression and weakness) and is also unable to feed the poor?

The able-bodied must fast. It is permissible for the sick to break their fast if fasting would worsen their illness or delay their recovery, and they must make up the missed days after they recover. As for a sick person whose recovery is not expected, they must feed one poor person for each day, and if they are unable to do so, then nothing is required of them.