Due to cancel UAE visa, am I eligible for Chinese visa?

I currently have a valid UAE visa (irish resident) but I am leaving my job soon so I will have it cancelled before I am due to enter China. I have not yet applied for the Chinese visa. Is it possible to enter China without a UAE visa that is valid for the next 6 months? If so, will I need a letter of no objection from my employer as my employment will be terminated soon?