My two year postdoc contract is ending next week. I am looking for a job at a bank in my state now. My university's personnel office has contacted me asking me to resign; that is to say, they're asking me to bring the employment relationship to an end (a few days) before the automatic end date in the contract. What should I do?
There is no need to resign if you have a fixed-term contract. When your contract ends, your employment ends. That's it.
Unless administration gives you a good reason, you don't need to consider this request any further. Since there is no possible advantage for you, you simply decline to do this.
 I'm assuming a normal western employment system. The answer might be different in places like, e.g., India, where employees have fewer rights.
- Read your employment contract and handbook very carefully. Particularly look for information about severance payments. Also check for information about notices that must be provided, and when they must be provided.
- If you are entitled to a severance payment, resigning will likely give up that payment. Do not do that.
- Do not agree to any document falsely claiming you have been provided with a notice. If you agree you received a notice, you may give up pay in lieu of notice.
- Find out about your local government's unemployment insurance/benefits. They may not apply if you resign.