"Is the house that we've been living in for 6 years, that will be inherited, considered part of my parents' estate for paying off debts?"
o If your folks own the house and you live there, you assume you'll inherit the house. That means that they must have a will that leaves it to you. If there are other potential heirs, you might want to make sure you will in fact inherit the house (especially if you've been paying all the costs for the house). You could have an estate planner for your folks confirm this.
o Make sure the property and casualty insurance is handled correctly. Are you listed as named insureds? If you have personal property in your parents house and the insurance is in their name, is your property covered? If you are actually tenants renting the house from them (you didn't say in the facts) then your parents should have landlord coverage and you should have tenant coverage. You could have a property and casualty insurance agent review this for you.
o If you're paying property taxes on the house because you're living there, and your parents aren't, you won't qualify for an income tax deduction for the property taxes because you have no ownership of the house. You might want to confirm this with your or your parents CPA and it might make sense to have you buy (or have your parents gift) some of the house to you so that you can qualify to deduct what you are paying for.
o If your parents own the house, then it is an asset in their estate and will be available to satisfy claims against their estate. You didn't indicate why you were concerned about this, or what types of claims, but your best bet is to discuss this with a local estate and probate attorney. Depending on the facts your parents might be able to sell or gift you interests in the house and remove some of the value from the reach of claimants. It might be possible that if you've been paying all the taxes and carrying costs on the house, have made and paid for improvements, etc. you might be able to argue that you should already own some percentage of the house because of this. If your parents are facing serious financial issues and the house is a significant asset you probably need to speak with a bankruptcy attorney so that if your parents are going to try to gift/sell the house to you now, or you're thinking of arguing that your absorbing costs for the house entitles you to ownership of some portion, that the transaction will withstand a challenge of your parents' claimants.
o If your parents are or may in the future receive governmental aid, then they should consult with an elder law attorney (this is a specialized speciality, not a general estate planner) as there may be special exceptions that can protect the house.
There are potentially a lot of issues for your parents and you, but taking care of them proactively will give you a better result.