How do we avoid the complications of a “long-fuse” resignation?

Q: One of our employees gave us a verbal notice of leaving our employ, but informed us she would have to sell her house first. It has been over six months, and we have hired her replacement so she could train. She has since submitted a written letter of resignation. Will we have any responsibility for unemployment benefits since we suggested it was time for her to submit that letter of resignation? She was not planning on giving us one until her house sold—it has not. – Tom, Illinois