If she hasn't already, an article in The LA Times titled “Consider tax implications when downsizing,” recommends that she needs to hire an experienced estate planning attorney who can help her evaluate her options.
If she sells, she could possibly be in for a shock because there might be a considerable capital gains tax on the sale. Federal law permits a set amount of capital gains on the sale of a primary residence ($250,000 per person) to be excluded from income. However, anything above that amount would be taxed heavily as a capital gain.
The capital gain is determined by the difference between the home’s sale proceeds and the seller’s tax basis in the home. In this scenario, at least half of the home receives a "step up" in basis to the then-current market value when the husband passed away. If the mom lives in a community property state, e.g., California, the entire property would have received this step up at his death. As a result, any increase in value since the husband’s death would be subject to capital gains tax (minus the $250,000 federal exclusion).
Keep in mind, that if the mom dies while still owning this house, her heirs would get a tax basis equal to the property's value at her death. So no matter what state she lived in, none of the house's appreciation during her lifetime would be subject to tax.
Tax issues alone shouldn't dictate what your parents decide, however you all should consult with an experienced estate planning attorney to learn about these and other issues in order to make an informed decision about their next steps.
Reference: LA Times (December 28, 2014) “Consider tax implications when downsizing”