Her ILR application will be refused. You really don't have any choice since it's already expired. Better get an immigration solicitor to help you and explain to you further your options. The members here prepare for such visa applications a year before the expiration to make sure they won't have any problems when application time comes.

Your wife is considered as an illegal now at the moment. She doesn't have a valid visa to stay here. I'm sorry to say but you can only blame yourselves for not preparing for this so much earlier than required.

Read this: https://www.freemovement.org.uk/over...pplying-leave/