When a couple is proceeding to divorce, what is the halacha if the wife realizes she does not possess her Kesuva as it may have been misplaced or lost? Can they still proceed with the Get process? What are the ramifications?
There is no problem in proceeding with the divorce.
The purpose of the Kesuba document is as proof: The woman proves how much her husband must pay in case of divorce (or death).
Today, the financial elements of a divorce are usually conducted by agreement and not by the Kesuba document. Although there is an obligation for a woman to keep possession of her Kesuba document, its loss will not generally affect matters of divorce. Moreover, the amount is often standard.