That is an excellent question.
When you conduct a short sale, you are asking the lender (usually an investor also) to take a loss on an investment that they made in good faith. You can understand that the lender's job, as the asset manager, is to minimize the loss, so they expect the owner of the property to participate in the loss.
Participation comes in different forms. They will want to see an financial statement, including all assets and liabilities. Assets including other real estate, as well as financial investments, 401ks, stocks, bonds, savings accounts, but also collectibles, valuables, cars, boats, etc.
In some cases, depending upon the amount of the loss, offering to take a promissory note for all or part of the shortfall might be a strategy that will protect your credit.
To your question, if there is equity in this property, they have potentially the right to find a way to get at it.