"In the event of death, resignation or disability of a nominee of the Party for President or Vice President after the adjournment of the National Convention, the National Chairperson of the Democratic National Committee shall confer with the Democratic leadership of the United States Congress and the Democratic Governors Association and shall report to the Democratic National Committee, which is authorized to fill the vacancy or vacancies."
They can pick anyone that damn well want after the convention is over.
Watch all of the polling spring up around convention time to get an idea of who the "dark horse" will be,
The advantage of doing it before the convention is that Democratic voters will feel like they had a convention that mattered—stirs up their juices—gets them motivated.
One of the big issues for Democratic voters these days is they are starting to get a clue that a very tiny elite runs their party.
An open convention would quell that perception—even if the reality might be different.