Unless the illness is fake, normally, we need to understand that every employee is a human being and as such, would fall ill to some illness or other. As such, it is not ethical to remove an employee just because he has fallen sick. As I mentioned, if the employee is faking it, you can take measures to see that he does not repeat the incident again in his career with you. However, I would suggest you talk to his previous employer to understand that his is not a case of frequent illness, in which case, you can ask him to undergo a medical check to ascertain why he is falling ill frequently.
To get back to your question, no, we cannot terminate an employee, even a new joinee, just on the basis of his falling ill.
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