If you have an illness and your supervisor says you can “take all the time that you need”, can you still be fired?

As a general matter, an employer may terminate an employee who misses work for illness if the employee is not using (or doesn't have) PTO to cover the absence, or is not qualified for and taking FMLA leave, or leave under a similar state law.

However, that said, IF you only took the time off because the employer promised you that you could take it off, you may have a claim against the employer for terminating you for relying on their promise; you would be suing under the theory of promissory estoppel, or that you did something to your detriment (taking time off from work, which led to your termination) in reasonable reliance on their promise that you could in fact take the time.

The employer could still terminate you for other reasons: e.g. poor performance, a restructuring, or if you lied to them about something (such as about the extent or nature of your illness, or your need for time off--for example, if you misled them as to the severity, they could terminate you). However, if there was not some other ground or reason for termination and if you only took the time off after being promised that you could, you may have a legal claim. If you think that's the case, you should consult with an employment attorney to evaluate the situation and your rights in greater detail.