Question: Is a contract valid if one party doesn't know the other has signed? For example one party signs a contract, faxes or emails it to the other party, but the other party doesn't reply. Can the other party play it to their advantage saying "we had agreed to this!" when it works for them and "we never signed this!" when it doesn't?

Answer: 
1. Fax or email

At this time in common law, faxes and email are considered to have been accepted when actually communicated to the other party. This means that if I sign a contract and send it to you, I acceptance of the offer is not actually effected until you read it.

2. Post

However, the postal acceptance rule can play havoc with this. Under this rule, and specifically for post, as long as there is some indication that we contemplated acceptance by post, my acceptance of the offer is effected *the moment I put it in the mailbox*, regardless of when or whether it actually reaches you.

Your scenario
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* A has signed a contract and faxes it to B
* B doesn't reply
* A or B tries to claim that they never agreed to this or signed this

### B has read the contract and was the offeree

If B claims not to have read it, A must prove that they have, or that acceptance was otherwise communicated to them. This is unless the postal acceptance rule applies, in which case it does not matter whether or not it was read. Proving that it was posted is a different matter.

### B hasn't read the contract or was not the offeree

* A was the offeree (A sent B a signed contract)

In this case, A must prove that they actually communicate a revocation of the offer. If B has not accepted the offer, then A can communicate this in any reasonable way.

If B has accepted the offer, then A must prove that the revocation was effected prior to their acceptance. Otherwise, A is bound by the contract.

* A and B drafted this contract together (offer and acceptance is unclear but there is clearly agreement at some point)

In this case, it's a bit murkier but it is likely that A would not be bound by the contract.
The signed contract is simply good evidence of the agreement you made, nothing more (that may not be true in all jurisdictions). If, as in your scenario, John sends Jane a contract, Jane signs and returns to John, and John doesn't respond:

* Jane should continue to communicate with John through all available channels that she has accepted and she considers the agreement in effect
* In the event that things go badly and John starts playing games and it's worth it to Jane to fight it rather than simply walk away and learn not to deal with John in the future - Jane sues, Jane shows the communications leading up to the contract, the copy with her signature, the communication in which she sent the contract to John, and the follow-up communications to the judge. Civil cases are won by a preponderance of the evidence. What evidence does John have? Shrugs his shoulders and lies to the judge? Judges are good at recognizing that. Keep records and you'll be alright.