Followed from this question: How was Rebekah able to enter the Salvatore home? , Elena is no longer owner of Salvatore house because she died once.
Now, the question: Who is new owner of Salvatore house? Elena doesn't have offspring, so what does law say? How do Salvatore brothers live in house as they are no longer invited? Can Salvatore brothers be thrown out of Salvatore house?
Legally speaking, when Elena dies, all of her possessions (her "estate") are divided up according to her will. Now, if I were living in Mystic Falls, I'd definitely have a will from the get go, but lets assume Elena is a typical teenager that isn't thinking that far ahead.
In that case, when she dies, her estate will be "intestate", and in most states, her possessions are divided up among her next of kin. Since her parents are both dead, and she has no children, that will be Jeremy. (If she still had a living legal guardian, I think she would have come first, but I'm not sure.) If she has no next of kin, in most states, her estate by default will revert to the state. They would probably then have an estate sale to liquidate her assets, in which case the home would go to the highest bidder.
Whoever ultimately gets it, the legal transfer happens at the point that Elena's estate is settled via a probate court. Since the law doesn't officially recognize undeath, I doubt a dead-but-not-anymore Elena is legally dead, so her possession still legally belong to her. After all, the Salvatores had to legally own their house in order to transfer the deed to Elena in the first place. We are now basically in the same situation as we were then: the property's legal owner no longer gives the house whatever intangible property it needs to keeps vampires out, so they can enter at will.
It is also unclear exactly how the legal aspects of inheritance would affect a vampire's ability to enter the house. Its never explicitly stated in TVD, but in other modern vampire mythologies, the house barrier depends on how ownership and possession. For example, the Harry Desden series describes this barrier as the threshold that builds up around someones emotional/spiritual "home", that separates the interior of someone's house from the "rest of the world". If a similar mechanic is at work in TVD, merely posessing the deed to house is not enough, Elena has to actively "take control" of it before she can invite/uninvite vampires. If Jeremey, for example, took no action to assume ownership of the house upon his sister's, that would leave it open. (Consider that, in general, someone owns almost every building in the US. Even abandoned ones have a name on their deed, even if its a local government that received it by default. They are simply ignored and neglected, and thus are not "homes" to anyone.)
It's also possible that there was some legal agreement in place accompanying the deed transfer that reverts the house to the Salvatore's upon Elena's death, but that's just speculation, and doesn't change much anyway.
No One owns the salvatore house, once Elena died the house no longer has an owner. That is why any vampire can enter the house without invitation and also why the Salvatore brothers originally gave the house to Elena.
