If you are fired from a job from which you provide for you and your family, and the firing prevents you from aquiring another job, and in turn you become homeless and destitute...then yes, being fired can cause PTSD (post traumatic stress disorder). The firing then becomes a life-threatening event, as you can no longer house, feed, or clothe yourself. When you have lost everything and you struggle to survive, the firing then becomes embedded into your mind, and you have frequent recollections of the event through flashbacks and nightmares.
The firing also makes your hypervigilant of others, especially those in authority. You become so suspicious of other people who could do you in, like your boss that fired you. So you may misinterpret others' help as a danger to your well-being.
Typically, PTSD has been described for people who have been exposed to life-threatening situations. Well, being fired and the resultant destitution is life-threatening, especially in Western, capitalist societies where there are inadequate safety nets to prevent people from going hungry and being homeless.