I am looking at contract, which the employer is telling me they do not have to sign. My understanding is that all parties in a contract should sign to acknowledge the read and agree to the terms. This is specially concerning to me since the terms of the contract are in review and modification. I am almost certain that this document needs to be signed by all stakeholders. Would you agree? Are there employment contracts or other agreements which are only signed by the employee?
Contracts do not need to be signed by anyone.
Among other things (see What is a contract and what is required for them to be valid?) all that is required to form a contract is the consent of the parties.
If they give you the employment terms then they have consented to them. If you start work, then you have assented to them. No signatures needed.
@DaleM is bang on in that contracts do not need to be signed by anyone (in most cases) to be valid. Further, no one can force you to sign an agreement - but I don't think the answer should stop there.
If the company is refusing to sign the contract, then I would be EXTREMELY cautious of proceeding - particularly if the contract has variances from a standard contract you can demonstrate they routinely use. The problem is that if there is an issue (and really, if there is no issue, then none of this matters) and the contractual terms are favorable to you, they can turn around and say there was no agreement, simply a counter-offer which they did not accept.
I might be inclined to find out WHY they are refusing to sign it - if they lack authority to sign, they lack authority to deal ! You may want to point out to them that you are willing for them to make it clear - where they sign - that they are signing as an officer of the company and not in there personal capacity if its an issue.
If you can't get an agreement, and you still want the agreement, maybe they would be OK with them acknowledging receipt of the agreement in an email - in that case I would scan the agreement, attach it to the email, Generate A SHA1 HASH of the scanned file and mention - it in the email - and ask them to reply with receipt of the message. MAKE SURE YOU KEEP A COPY OF THE FILE - if there is later doubt as to the version they were accepting you can probably use this to establish the exact version of the contract.