It's great that she owns her home. Most minimum wage earners don't, and won't on that pay scale. Also, I believe your mom isn't paying any income tax on that $13,000, so that's her net income? Someone earning minimum wage pays state and federal income taxes, and social security & Medicare. And rent. Yes, I'm sure your mom pays property taxes; on the other hand, while sure, she's technically a single parent now, she's not raising/supporting children on that small income.
And while it's absolutely NONE of our business, it's entirely possible she has savings, investments, retirement/pension, life insurance, annuity, help from her children, or any combination of these. Most single parents earning minimum wage don't have alternatives.