That might be a problem if you've only got enough money for this month's rent, but otherwise any company that would pull that would abuse you in other ways had you been hired.
Speaking of rent, you can often negotiate that as well! When I was living in an apartment, any time there was a rent increase, I would go into the leasing office and ask if they could do anything about the increase. I always walked away with knocking around $100 off the monthly rent.