Both parents passed with a week of each other and both were on Medicaid - can we sell their house to pay ourselves back for funeral expenses?

You might want to check with a lawyer to find out if you can file a lien on the estate to recover your costs.

To me there’s 3 different but interwoven problems:
- the estate recovery that Medicaid can do as both parents were on Medicaid. & by being on Medicaid the state can place a lien or a claim on the property to repay or recover costs paid throughout medicaid. The lien or claim can place a cloud on the title so property cannot be sold with a guaranteed ownership. How much $$$ did medicaid pay?.....I’d bet it’s way way beyond the 12k the house is worth!
&
- If they both died without a will, it’s considered an “intestate” death. Most intestate have it so all assets escheat to the state. If your state does this system, you would have to establish your right & position as a heir before - like through a lineal heirship filing process - you can sell property owned by your parents. You legally cannot sell the house as you are not the owner. You will need an atty to do a lineal heirship or have you named as administrator of parents estate in probate court. 
&
- funeral costs (15k) paid can become a debt of the estate IF probate is opened. You need something legally formal to which to submit your costs to; & that’s what probate can do. Otherwise it’s a cost family gifted. So if probate opened, the 15k funeral costs get entered as a debt (or claim)by whomever paid them. Also whomever pays property taxes, property insurance can also enter those as a debt / claim. But you’d need to open probate & that means you need an atty as there’s no valid will. (If there was a will, you might probably - if your comfortable in a courthouse and somewhat legally savvy - could file a small estates affidavit or do muniment of title & get house sold, but you cannot as there’s no will....).

If house is really worth 12k, if it were me, I’d just walk on doing anything and not spend another dime or time on this 12k property as every day there’s costs on all this. You will never ever be in the black $$wise. There will be atty & court costs to establish a lineal; AND property taxes - hopefully your folks are current on property taxes as these have hefty interest and tax sales happen for all delinquencies; AND any other house costs (insurance, utilities, maintenance); plus Realtor commission to sell at Fair Market Value. Added up could easily be another 5k, 8k, 10k or more. That “estate” is already in the red 3k, there’s not ANY real profitability here EVER. Move on & maybe ask family to chip in to you directly to offset the 15k funeral costs.

House becomes a problem for county & state. 
No will = assets escheat to state.
It’s their monkey and it’s not an adorably cute baby Langur monkey.

Keep in mind that if you decide to become “responsible”, like be named administrator or executor of the “estate”, that means dealing with whatever the state or its outside contractor starts sending out on MERP / Recovery as both parents were on Medicaid. MERP will need to be dealt with cause if not, their lien or claim will cloud the title on the house so it cannot be sold till cloud is lifted. MERP would likely fall into the not cost effective to be done by the 3k/10k cost benefit guidelines but there will be a pile of paperwork to get done before ever getting to that point. And times 2. Your time has a value which that 12k house will never ever compensate for or cover the costs needed to do a legal process unless it has a very unique to you priceless value. 

My suggestion is walk away, let it become states monkey to deal with.

Doesn't this get complicated? Yes, as ff says, talk to Medicaid.

RevMullins, depending on your State laws regarding Probate, Medicaid could be first in line if Medicaid had placed a lien on your parents house. Medicaid would like to be reimbursed for the care they had given your parents. Again, this varies from State to State. Do not sell the house without checking first with Medicaid.