According to the commentary at the bottom of the Artscroll TaNa"Ch, in the beginning of the book of Ruth, Na'omi attempted to dissuade her daughters-in-law from following and staying connected to her because she was being punished severely for her sins, and they'd only suffer by their association with her. The commentary states (1:13):
Realizing that they wanted to go with her, Na'omi said, "I cannot bear to see you suffer on my account, for you are sinless; it was for my sins that [G-d] has been punishing me."
This does not seem to be the plain meaning of the verse. In fact, even the Artscroll's own translation renders it:
...I am very embittered on account of you, for the hand of Hashem has gone forth against me.
1: Where does Artscroll get that she is stating that her life is bitter because of her sins and that it would harm her daughters-in-law to stay with her?
2: What were her sins? According to a plain reading of the first few verses, Elimelech is the one who took the family out of Eretz Yisrael. The Alshich* and the sources he cites explain why Elimelech's actions were so bad as to deserve death. But nowhere do I see (yet) anything making the case that Na'omi was his co-equal sinner. The closest I've seen so far is that she is kept alive so that she can be a mentor and guide to Ruth, whose family tree will eventually yield David and the royal family. So what exactly did she do wrong?
*(I've only looked in the Alshich so far, because Artscroll quotes him quite a bit in its commentary, and it also happens to be the only other commentary I have handy.)