Are there any legit business that would oversee a disabled individual (in terms of payment etc provided by parents, once their parents are deceased?

Yes, there are a  number of legitimate businesses who focus on managing fund for the benefit of disabled persons and making sure that their needs are provided for. These tend to fall into two basic categories: community pooled trust companies (an example of one of those is Commonwealth Community Trust) and corporate fiduciaries (a category that comprises both banks and brokerage firms that have trust departments and independent trust companies). A trust created for a disabled person's benefit is usually referred to as a "supplemental needs trust" or a "special needs trusts," and those also fall into two different categories: first party (those funded with assets that belong to the disabled person) and third part (ones funded with money from someone who is not the disabled beneficiary, such as a parent). Not all corporate fiduciaries handle supplemental needs trusts. An example of a corporate fiduciary that does handle supplemental needs trusts is Southeastern Trust Company. If you want to provide for your daughter's benefit, the best thing to do is find an experienced estate planning attorney who can help you establish a third party funded supplemental needs trust. Most such attorneys know of companies that can serve as trustee for your daughter's trust and can make recommendations.

There are master pooled trusts, some national, some regional, some state.  The ARC (of Georgia, of Texas, etc.) is generally highly recommended.  See whether it or other master pooled trusts in your state would be appropriate.