If the driver forgets to start the ride it is on the driver. Uber (X and black) will not correct fares for our errors, but if a passenger emails to complain the route was long or the driver forgot to stop then Uber will adjust the fare.
There is a Fare Review button we can hit instead of going online after a ride and that can add tolls and such (no tolls here so I've never used that part) or to flag customers who are going to need to be charged cleaning fees, but we can't just add to the fare.
If the driver completely forgets what some do is to do the route backwards. I don't do that because then savvy customers may not understand what is going on but will notice they have not received a receipt yet.
Lyft, on the other hand, will always use the pick up point as the start of the ride so if the pickup point the passenger gives (due to bad GPS lock) is off the passenger will be charged more that they should.