Right now there is no law that if LE finds remains, that they have to have DNA testing completed on it. (That costs quite a bit of money) Usually once remains are found, area LE will be notified and they will search their missing persons reports. If no potential match is found the remains will usually be held at the coroner's office for a time, then eventually may be buried or cremated. The info on the remains is kept on file, in case someone comes looking for info later. Some depts are doing the testing, and some depts do not.
The FBI has a database set up, where families of missing people can request that the DNA of their missing person be filed, in case remains are found somewhere and can be processed against this for a possible match.
If a dept processes the DNA on some remains, they will usually enter the DNA report in this looking for a potential match. However there is no law that says that missing persons DNA must be entered here, nor any law that requires any dept to get the DNA on any remains that are found.
A woman in Ohio was working on a law to require that all remains be tested. I don't know if she was working on this at a state or federal level. And I don't know how far she got, I haven't heard anything for a few months. If anyone is interested in helping with this I will see if I can get more info.