Although nothing is set in stone yet, according to The Wrap, Universal is currently considering scrapping production that was already completed on Fast & Furious 7 prior to the tragic death of franchise star Paul Walker, and restarting filming entirely with his character written out of the story. From the report:
Because the studio is insured for unexpected losses such as this one, the cost of scrapping the production is not a central factor. The studio would likely be made whole on that cost.
One viable option would be to start over. One individual said they were considering making the movie without Walker’s character, Brian O’Conner. But another individual said that option was not under consideration.
This solution really would make the most sense. Though it's been reported that many of Walker's key scenes had already been filmed, but there was still a lot left to shoot—and a rewrite at this stage to write out his character without a proper send off wouldn't make sense considering how important he was to the franchise. If the studio is covered by insurance, this option seems the most respectful to both Walker and the fans.
Once again, though, nothing has been officially decided yet—in fact, the only thing that Universal has revealed is that production on the film has officially shut down for the time being as they decide how to move forward. According to a statement:
Right now, all of us at Universal are dedicated to providing support to Paul's immediate family and our extended Fast & Furious family of cast, crew and filmmakers. At this time we feel it is our responsibility to shut down production on Fast & Furious 7 for a period of time so we can assess all options available to move forward with the franchise. We are committed to keeping Fast & Furious fans informed, and we will provide further information to them when we have it. Until then, we know they join us in mourning the passing of our dear friend Paul Walker.
We'll keep you updated on this story as it develops.