It is possible to establish sufficient financial resources other than by income.
The most common method to establish sufficient financial resources other than by income is by value of your assets... or the assets of the intending immigrant. When we pursue this as the avenue of sponsorship, we ask that the assets be definitively documented and even so, we prepare for the possibility of a Request for Further Evidence (and thereby a potential delay in processing of the application).
If you would like to pursue this option, excellent documentation of your assets should be prepared. This will particularly be the case when the assets are being used not to SUPPLEMENT an income below the required levels, but to entirely REPLACE the income requirements of sponsorship. This will result in a heightened level of scrutiny.
Click on the below link for a brief description of the rules regarding the use of assets to prove ability to support the intending immigrant. Please note that the rules say that only assets that can be converted readily into cash within one year and without considerable financial hardship can be included. In practical terms, this generally means only the intending immigrant's property can be considered given that you the intending immigrant and the petitioner usually intend to live in the petitioner's home in the U.S. Additionally, because of the current situation with the housing market and especially if there is a mortgage on the property, a home may or may not qualify to be counted as an asset. A recent appraisal must be included, regardless.
Finally, automobiles may not be counted unless you are in possession of more than one vehicle.
So, if the U.S. petitioner is not working, you will need to show substantially documented assets in which either the petitioner or intending immigrant has full or majority equity ownership and those assets must be recently appraised and well documented.