You have a right to collect rent until the sale is completed. You also have an obligation to make the mortgage payments you promised to pay until you are released from that obligation. If you fail to live up to your legal obligations, there may be consequences. If you are unclear about your rights and responsibilities, you should consult a lawyer in your area who is experienced in foreclosure defense.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. Actual legal advice can only be provided after completing a comprehensive consultation in which all of the relevant facts are discussed and reviewed.
Typically to apply for the short sale, the lender will have required you to have stopped paying the mortgage. Afterall you are stating to the lender that your financial position does not permit you to continue making payments. Consult with a knowledgeable short sale attorney to counsel you.
In California typically those who are seeking to short sale stop making their payments, as this shows the hardship they are experiencing. However you need to be prepared with what you can do and what your options or the ramifications are if the short sale is denied and you can not catch up on the payments. This is why you should seek the advice of a real estate attorney in your state.
In addition to AVVO's disclaimer, please note that by giving this answer no attorney client relationship is intended or entered into and unless there is a signed fee agreement in place, neither myself nor anyone in my firm has intended to solicit clients nor do we represent them. The answers are general in nature and may be given without weighing or knowing all of the specifics of any particular question or situation. No answer should be relied on in whole or in part, in a decision to act or not to act in pursuit of any potential claims or actions. You should always consult with and obtain the advice or representation of a licensed attorney in your state to protect your rights regarding your case or matter.