Legally yes but many companies don’t want litigation in cases where a former employee can sue for slander. Most companies have policies that will say position held at termination and how long you were employed. Some will say eligible or not eligible for rehire but there are many reasons you may not be eligible. I’m assuming you’re asking this question because of a firing.

Large companies outsource these referrals to a third party company called the work number. This is considered a credit bureau for legal purposes and you can request a copy of your file