Here is Marina's account to the HSCA of her discussions with Oswald about him going to Mexico City and what would then happen to her. She had remarried and taken the Porter name.
Mr. McDONALD - What was your reaction to this whole affair, going to Mexico City, going back to Dallas
Mrs. PORTER/MARINA - I was very upset about it. I did not know if I would see Lee again. I had to be responsible for one child and I had expecting another one. So, anyway, I was quite lost. On top of everything, I could not share that with no one.
Mr. McDONALD - Could you share it with Ruth Paine?
Mrs. PORTER/MARINA - No.
Mr. McDONALD - Why do you say that?
Mrs. PORTER/MARINA - Well, I don't know why, but I was not approved of what Lee did, but at the same time he was my husband and I have to be somehow loyal to him.
Mr. McDONALD/MARINA - When he left for Mexico City, when you both parted in New Orleans, when did you expect to see him again?
Mrs. PORTER/MARINA - I honestly did not expect to see him again, but he said that if his trip to the Cuban Embassy would be unsuccessful and they would not permit him to go to Cuba, then he would come back to Ruth Paine's house in Irving, Tex.
Mr. McDONALD - That he would not come back?
Mrs. PORTER/MARINA - He will come back.
Mr. McDONALD - You are saying--the question was, when did you expect to see him again?
Mrs. PORTER/MARINA - In the matter of a week.
Mr. McDONALD - You did expect him to come back?
Mrs. PORTER/MARINA - Well, if he did, it was understood if he can go to Cuba right away, he will go, but if he can't, then he come back to Texas.
Mr. McDONALD - If he had been successful in getting to Cuba right away, what was your plan? What were you to do?
Mrs. PORTER/MARINA - Well, he said that he will be in touch with me and send for me to follow him to Cuba.
Mr. McDONALD - Did he ever discuss if he were unsuccessful in getting into Cuba, that he would try to go back to the Soviet Union from Mexico City?
Mrs. PORTER/MARINA - Yes, that was discussed, too.
Mr. McDONALD/MARINA - At that point was he willing to go back to the Soviet Union?
Mrs. PORTER/MARINA - As far as I remember right now, I think, yes.
So when he came back from the failed attempt to get into Cuba he sent a letter to the Soviet Embassy in Washington asking them to process his visa application. He was still willing - if Marina is correct - to go to the USSR. But the Soviet officials had decided to reject his (and Marina's) application. Oswald was stuck in the US, a country whose political and economic systems he said were part of a "slave" system.
Link/testimony:
http://mcadams.posc.mu.edu/russ/m_j_russ/hscamar2.htm