When it is a primary home any loan against the property would require the loan to meet federal abilty to repay (ATR) requirements. That abilty to repay does not have to be just paystubs and tax returns. Self employed can use bank statments for example, Asset depleation is another approach for borrowers with little income but a lot of assets.
We also do the occasional no doc loan on a primary home through CDFI banks. The rates on the no doc loans as you might expect are high, but if they have decent equity and good credit it is an option for borrowers without much other options.
The last option would be a Home equity investment (HEI) but these can be expensive and should only be used in my opnion if credit would preclude any other option.