If the furnace died and she needed to pay half a year or more of income to replace it she would be in a bad place financially.
Because she has such a low income to get a mortgage over $150 a month would be most unwise. And at that rate it would be well under $25k. More likely to be safe it would be about $15k purchase price. That pretty much says only a trailer on a rented lot. Since lot rent could be $300 or more a month (without a trailer) she should not buy.
I am sorry, I know the numbers. With the cost of heat, electricity, food, and something added like clothes and doing anything that income is just NOT enough to do it. Check into section 8 housing it takes about 1/4 of her income and that she could afford.