When I was arranging to leave my retail job and find another, the person from the new job gave me a date to start on. It coincided with my 2 week's notice. The thing is, what if I didn't put in my 2 week's notice for my old job? Wouldn't I be fucked if I just up and left for another job without much notice? In the future, if another employer gives me a start date that coincides with the job I'm trying to leave, what do I do/say?

Because it's foolish to put in your 2-week's and not know if the new job will take you