If someone has been working very hard at work, we might end our conversation or email with" Bye. Don't get too tired/ don't work too hard" Sometimes this can be said sarcastically as well to someone who is very lazy at work.

I think I will start saying that from now!~

You can ask them if they are feeling alright but never say directly "don't be tired". I would like to ask you ,if you say something similar to 'don't be tired' in Azeri??

It seems that we have similar culture. In China, we usually say " 别太累", which means " don't be too tired". We care more about his/her health than his/her work. We hope that he would have a good rest so that he can continue to work next day. We don't hope that he is too tired or ill because of hard work.

No, we don't say anything like that. Just as Eliot had responded, we mostly say "Goodbye" or "See you" as well as "Have a good night/good day"