your husband is your sponsor, and effectively he's withdrawing his support if he says the marriage is over and will not sign her ilr app.
that's why the wife should apply for ilr asap, to protect herself and her rights to remain in the UK, many if not all have left their home they grew up in,to come and make a new start in the UK and now the UK is their home.
if she had a child that could help her case..
2 yrs on a spouse visa you can apply for ilr, but those married to a European in the uk you need to be married at least 3yrs and at least the final year you needed to have lived in the uk, and you need help from your ex (which many refuse to do) if you want to stay in the uk should your marriage break up.