What happens when input current in common base amplifier circuit is increased?
As \$R_E\$ is decreased, \$V_{out}\$ will increase, up to a point. When \$V_{out}\$ approaches \$V_{cc}-0.7V\$, the transistor will begin to enter saturation. \$V_{out}\$ will increase more slowly. \$V_{out}\$ will not increase much more than \$V_{cc}-0.2V\$. [Here I am using \$V_{cc}\$ to represent the voltage of the right hand side battery.]
If \$R_E\$ is made sufficiently low, and if \$V_{in}\$ is greater than 0.7V, then the base-emitter junction of the transistor will eventually have excessive current, and the transistor can be destroyed.