Julie,
I concur with Steve's answer here that a reverse mortgage may be an appealing step - it is a way for you to borrow money on the residence to pay for the expansion (and possibly other care and needs as well), without requiring a monthly payment on the debt (although it will have to be paid off from the sales proceeds of the home when your parents eventually pass away). However, you will likely want to explore using other available assets first, if that's feasible - a reverse mortgage can be an expensive solution compared to using other assets, although it's still a very appealing solution to allow your parents to stay in the home if you truly need to tap the equity in the home.
However, I presume the reality is that the property is in your parents' name, not your own. Consequently, you're not able to borrow money on their property directly. Instead, you'll need to have them go through the process of applying for a reverse mortgage to receive it.
If your parents aren't competent at this point to be able to make their own decisions or handle their own financial matters, the next question is whether there is a Power of Attorney document in place that names someone to act in their stead. If the Power of Attorney document authorizes you to act on their behalf, including the power to borrow money, you should be able to proceed utilizing the power of attorney document (although you'll need to find an experience mortgage broker who knows how to handle this less-common situation).
If your parents don't have a Power of Attorney document in place, then you will need to get in touch with an estate or elder care attorney in your area to determine how to proceed, as the rules from that point forward (acting as a guardian for your parents to handle their financial matters) will vary depending on the state and county that you're in. Working with an attorney may also help if there's a possibility that your parents will require Medicaid in the future, as the attorney can help you plan around how to ensure properly eligibility for Medicaid and that you don't accidentally take any steps that could disqualify your parents unnecessarily.
I hope that helps a little!