Not unlawful termination, most likely. The employer can terminate for just about any reason they feel like if it does not violate EEOC statutes or some other of the very specific protected class and situation issues.
What causes confusion in some cases is that if terminated for being out sick with a doctor's statement, you can file for and in most cases will have a very good chance for being approved for unemployment insurance.
The employer may not see it so, but unemployment insurance law most cases sees an illness as something the claimant did not have control over. Of course this has to be documented by a doctor's statement, but even if you were in danger of being fired, were over the attendance points, or were really needed at work, they assume you did not get sick or have a family medical crisis deliberately.