If a muggle born were to reject a letter from Hogwarts, do you think the Ministry would have to intervene?

We know that young children can do magic without knowing it when their emotions run high, would this eventually stop once they reached a certain age? I was always under the impression that Hogwarts/a proper learning of magic, is what stopped those magical outburts. But if a muggle born rejected to be taught magic, they'd be going around all their life unable to stop themselves from making things blow up (like their evil aunt!)

So if this is the case, do you think the ministry would step in, and if they did, what would they do? You can't force a person to attend Hogwarts... but it could also destroy their cover if they leave a muggle born unaware.