It is possible that the same thing happened to them that happened to the Dursley's. However, instead of sending lots of letters in hopes that the muggleborn student gets the letters, they send a lot of professors to explain about their world. They may explain that their child needs to be trained and that there will only be more accidental magic, but this time stronger, since they are at full magical maturity and they need a wand to help channel it properly. They come with a few examples via pictures (unmoving, of course) to show the damage done by accidental magic beyond the age of 10. They might explain about the trouble that muggleborns living in the muggle world without training would have to face, especially with the people who are hell bent on killing muggles and muggleborns.
However, it is possible that attending Hogwarts is optional and not required for mastery of magical talents. So, muggles who refuse to send their magical children to Hogwarts may be able to have a tutor for their magical child so that their child would be able to control at least part of their magic while still being able to attend their desired muggle school. Hagrid gave Harry the option of staying with the Dursleys instead of going out to get his school supplies,but that was the movie and Harry didn't want to stay with the Dursleys anymore. They may also give the option of having a magical guardian who would pick up their child and take them to Diagon Alley and help them to shop. That way their muggle parents never have to have any connection to the magical world.
However, the parents who refuse to send their magical child to Hogwarts may also be the ones who are abusing their magical child based on their magical abilities, like the Dursleys did to Harry. The person in charge of that child should then go and try to find evidence of abuse and report any found to the ministry of magic or any muggle police that may help the child escape from that environment. Vernon Dursley mentioned trying to stamp out the magic on two occasions, which showed evidence that he was willing to hurt Harry to ensure that Harry was "normal." He also refused to send Harry to Hogwarts, but Hagrid said that a muggle like him wasn't going to stop him. This may not be the reaction that the professors who go to explain the magical world to the muggleborns and their reluctant parents, since the Dursleys had no real say in whether or not Harry went to Hogwarts, while the muggleborn's parents were their biological parents and not just guardians.