I'm sorry to say this, but this is one of the saddest things a person can say in my opinion. You can definitely become your job, but I can't see myself ever wanting something like that.
A teacher impressed on me at a formative age that I wasn't likeable enough that people would ever respect me unless I did good work. I'm definitely reliant on my work (though no particular job) as a core part of my identity, but it's a mutually beneficial relationship overall. Tough love but insightful/fair advice in retrospect.