Can anyone tell me why rabekka is aloud in stephans house without being invited, because its under Elena's name and she didnt invite her in???

Elena died in 2x21 and came back to life, so anyone can enter the boarding house. That's how Katherine got there to give Damon Klaus' blood in the season 2 finale.

Elena berkata she would be the owner of the house for a short time ;) i think she´s not anymore because she didn´t needed it anymore

im guessing its somthing about her being an origanal that she can get in anywhere