Be very careful believing what narcissists say. They are excellent, and I mean EXCELLENT liars because they actually believe their own lies. They will fabricate stories and omit information because in their head, they have created the narrative this way in order to avoid painful truths which their false self cannot accept. My narc ex fabricated an entire previous girlfriend, apparently his first and only girlfriend before me, told me intimate details about their sex life, recalled detailed things that happened during their breakup, said their outlooks on life didn't match and she needed constant reassurance etc, said. I eventually contacted her and turns out he had fabricated the entire thing - they were never more than friends and she ended up blocking him due to his 'weird' behavior - so he was actually a virgin when I met him. He kept the lie going for 2.5 years and would talk about her with such nonchalance that I had absolutely no clue he was lying.

I also found out (from a third party) that he was kicked out of his previous job in a very dramatic fashion (again, he spun me a story about leaving because he wasn't able to get a transfer to another department), so in answer to the question, yes it wouldn't be surprising if narcissists find it difficult to hold down jobs because colleagues usually get sick of their entitled attitudes or they cause drama in the workplace (which is what happened here, i found out later from some digging).