Employer stated a 401k on offer letter but has not provided. What are the employees rights?

Is a company in breach of contract if they specifically state that the employee is entitled to a 401k but never provides even after being asked repeatedly when the eligibility period has already passed?

Way too many questions to effectively answer this.  1)  Does the employer actually have a 401(k), or were they indicating they would start one?  If the former, then there may be an operational failure for the plan, and missed opportunity corrections required.  If the latter, there actually is nothing that says an employer must have a 401(k) plan, so that leads to: 2) What was the nature of the "offer"?  If it rises to the level of an "employment contract" then there may be some remedy - but: a) that depends on the state in which the contract was entered into (state law governs employment contracts); and b) I'm not sure what the remedy would be, but I'm pretty sure suing for enforcement might be a career limiting move.

If you know the employer's EIN you may be able to check here to see if there is a Form 5500 for a retirement plan https://www.efast.dol.gov/portal/app/disseminatePublic?execution=e1s1

You would input the EIN (without dashes). 

It is possible to search by name, but I find the results are less consistent. 

Absence of a Form 5500 doesn't necessarily mean they don't have a 401(k) plan, as there are a variety of reasons why it might not show up, but if there is one listed, you should be able to request a copy of the summary plan description(ask in writing). If they don't give you one, you should ask why - usually the only reason would be if you aren't an eligible participant. 

1. Do they have a 401(k)?

2. Under its terms, is the person you are asking for eligible for it?

If they promised, but they have none, or they have one but would need to amend it to include this person, then I believe that there is at least one case in one circuit that says the promise is unenforceable because preempted by ERISA, which does not address. I don't know if that is the right answer. Keep pushing on both facts and law.

Do you have a letter or other writing that would show the promise?