Most employers ask that the potential employee sign the offer prior to starting work. Then, on the first day of work there is a slew of paperwork to sign. However, some companies allow you to sign all of the papers on your first day. Some professions, like teachers, ask that you do the majority of your paperwork prior to your first day. My suggestion is to ask when the company offering you the job is wanting to have the signed offer back. Then you will be working with facts and not suppositions.
If you ask you will be able to keep an eye out for these things.