When can upgrades be obtained or edited?
I think you're reading this too literally.
"Once runners have earned Karma..." is just an answer to "When do I start buying upgrades, in general?"  

For each runner, their earned Karma is a permanent value.
If you earn 3 Karma from completing a mission, that's 3 Karma that this runner will always have. This runner "has earned karma", now and forevermore.
Each runner is always "worth" as much karma as he has ever earned.  

Between missions, each runner can "spend" their karma to buy or swap abilities on their sheet (by the costing rules).  (the term "spend" isn't exactly right either; your karma is just your maximum capacity for upgrades, but it never goes away)
Even if they didn't gain any new karma on that specific mission.