I'd have to agree with OG.
The whole point to food stamps and Section 8 are that they are programs available for those who have very low income and assets to use for food and housing.
If she co-applies for the home equity loan with you, then it means that line of credit will be available just as much for her use as for yours. Those funds would need to be included as assets that could be used to pay for that same food and housing that the government programs are covering for her now. If the loan is significant (and since it is a home equity loan, we are probably talking several thousand dollars at the very least), then as a major asset, she could end up losing her food stamps and Section 8 benefits.