Re: Contract still valid?
Nice try. Assuming that the manager was authorized to enter contracts on the company's behalf, her signature bound the company, not her. The company remains a party to the contract regardless of her subsequent employment status.
Imagine if things worked the way you suggest. Every time such an employee resigned, all of the contracts he or she ever signed would suddenly become invalid -- and the other parties to those contracts likely wouldn't even know. The company would then have to renegotiate hundreds or even thousands of contracts simultaneously, losing many clients in the process and getting less favorable terms with many others. The problems such a resignation might cause would be so severe that these employees could essentially blackmail their employers by threatening to resign unless they got huge raises, bonuses, etc.
At the same time, a company that didn't like the terms it had previously accepted could get out of them by simply firing the person who signed those contracts. If you got a good deal on health insurance, for example, would you want to see that deal disappear just because the employee who signed off on it is fired, quits, retires, dies, etc.?
The reason we have contracts is so each party knows what he/she/it can expect from the others in the future. The system you envision would offer no such certainty. It would thus defeat much of the purpose contracts are designed to serve.