Let's say there two players on a server:

• Player1 with UUID of 11111111-1111-1111-1111-111111111111
• Player2 with UUID of 2222222-2222-2222-2222-22222222222

There is a scoreboard objective score and it's displayed on sidebar
The command /scoreboard players set Player1 score 20 is executed. This is normally visible on the sidebar: Player1 20
The score of Player2 is set to 50

The players are 15 blocks apart (outside of visible range for belowName)

The command /scoreboard objectives setdisplay belowName score was executed.
Player2 looks away form Player1 (Player1 isn't visible)

Player1 walks within 10 blocks (inside visible range for belowName) of Player2
Player1 now sees 0 score under Player2's name. Player1's sidebar contains the following:

Notice Player2's UUID with a score 0

Player2 now looks at Player1 and sees 0 score under Player1's name. Player2's scoreboard now contains:

Executing /scoreboard players list shows only Player1 and Player2

Player1's scoreboard stays the same.
Changing score for Player1 or Player2 doesn't chenge the score displayer in belowName

The following command is executed
/scoreboard players set 11111111-1111-1111-1111-111111111111 score 5
This command doesn't change the score of Player1, it stays at 20

Player2 now sees 5 score under Player1's name.

Both Player1 and Player2 have 11111111-1111-1111-1111-111111111111 5 in their sidebar. (Player2 donesn't have two 11111111-1111-1111-1111-111111111111 entries)

If Player1 moves more than 10 blocks from Player2, Player1 still sees 2222222-2222-2222-2222-22222222222 in his scoreboard. Upon relogging, the entry disapears (if they further than 10 blocks away). The entry reapears as soon as Player1 sees {{0 score} under Player2's name.

scoreboard setdisplay list and sidebar work normally.