Q. Allaah the Mighty and Majestic said in Suratul Baqara: “Divorce is two times,” and then he said after that: “So if he divorces her, then she is not permissible for him until she is married to another man,” meaning if he divorces her the third divorce. Question is: The prohibition of taking her back after the third divorce is before the iddah [waiting period] ends, or the prohibition is after it ends?
A. After the third divorce there is not taking her back. Returning / Taking her back is after the first and the second divorce, as per His words: “Divorce is two times,” meaning these two divorces are the ones in which there is ‘taking back’. So if he divorces her once, he can take her back before the iddah ends. Likewise if it’s the second divorce he can take her back before the iddah ends. Once she finishes the iddah [without him taking her back] in the first or second divorce, [and he wants to marry her] then he becomes a proposer just like another person [if she agrees to him, they do another contract of marriage with dowry and e.t.c]
As for after the third divorce, there is no return for him until after she gets married to another man -a proper marriage of consent and willingness- . Then if this other husband divorces her, he is allowed to marry her. And now he has three new divorces which are applicable between them.
Q. What is the benefit for the women in staying for the iddah [waiting period] after the third divorce?
A. The iddah in the third is for the purpose of making sure that she is not pregnant. As for in the first and second divorce [in addition to the same purpose], it is also for having a period of time for reconciliation for the one who wants to.
Source: Explanation of Sunan Abu Dawud
A Benefit A Day Keeps Ignorance Away 
I can understand that Iddah is the period where reconciliation can occur after the first two divorces. But what is the logic in making the wife stay in the (now) ex-husband’s house after the THIRD iddah? He has been married to her and has had conjugal rights with her all this time. There is obviously attraction between the two. If he is haram for her then how can she stay in his house? That part is very confusing.
The woman does not stay in the house after the third divorce.