I still think Elena was ill somehow. If not, she would have played doubles. It's a dead rubber match, and it's like playing for pride. Thus, if nothing wrong with her health, she would have played.
You are right that there might be other factors. Money can affect his decision, but I don't think he lost faith in her cuz Tarpishev almost chose Lina K. to be Elena's double partner (if he did not lie about this). Elena is a great and dangerous player. She could definitely have won over Mary if she had played. She is one of the top Russian players at the moment.
I found her interview at YEC about playing Fed Cup on Euro Sport website. She said "I really like this tournament. I am very proud to play for Russia. It's the last tournament but the biggest one of the year. I will do my best, and I hope we will win this time." She was really happy to play for her country but something happened. No matter what it is, it's really sad.