Voldemort couldn't kill Harry as long as he called the Dursleys home. Why didn't he just murder the Dursleys? This would prevent Harry from being able to live there.
['https://scifi.stackexchange.com/questions/114415', 'https://scifi.stackexchange.com', 'https://scifi.stackexchange.com/users/55866/']
The traditional fanon answer is "there were blood wards protecting the house". It would not, however, have stopped Voldemort (or his Death Eaters) from attacking the Dursleys when they were out (as proved by Umbridge's dementor attack).

That said, Voldemort would have needed to figure out 1) that Harry lived at the Dursleys (which itself might not have been common knowledge), and 2) that the blood protection was tied to that fact (that's assuming it was, which we only have Dumbledore's word on, IIRC, so that might not even be true).  

And after the ritual at the end of Harry's fourth year, Voldemort, specifically, had little to worry about from the blood protection anyway.
What would he achieve with this? 

According to Dumbledore:

> 
> The magic I evoked fifteen years ago means that Harry has powerful
>  protection while he can still call this house ‘home.’
> 
> 
> 

Harry and Aunt Marge are the only living relatives of the Dursleys. So if the Dursleys are killed, then Harry will inherit the house or part of it.

Technically he will be still able to call the house his 'home' and the protection will stay.

There is also the possibility that Vernon and Petunia Dursley created a will that explicitly transfers the full ownership of the house to Aunt Marge in case they are all dead. In this case the Order of the Phoenix will have hard time persuading Aunt Marge to invite Harry to stay until he is seventeen.

Still I find this unlikely. Even the Dursleys, as horrible as they are, would not plan for what happens AFTER the death of their only child.