If you didn't purchase CS6 but only ran the trial version then yes it won't work anymore. Nor will any of the CC versions if you have discontinued your Cloud subscription.
I suspect that when you cancel a subscription, any trials you are running that have exceeded the single month that they normally run for will be terminated immediately, regardless of when the subscription itself appears to finish. If the trial hasn't technically finished, you should be able to download the latest version and run that. If you can't, then you might have some grounds for complaining...