Still Getting Paid But Not Working

Hello! I live in the US, specifically the state of Ohio. I did work for a company where I traveled and received a monthly reimbursement for travel from a third party company. I have since stopped working for my employer, I do not get paid by this company anymore or receive any benefits. However, I still receive my monthly stipend from this third party company. There is no option to deactivate my account from my app or the website, I called the third party company and they said they cannot deactivate my account, only my previous employer can. I plan on sending one email to my old HR department to ask them to deactivate my account. If they fail to do so, could I be liable to return all of the extra money I received from the third party company? Or would that be the responsibility of my previous employer for their negligence in completing paperwork? Thank you in advance for any advice!