First I set up an objective.

Then I assign a score for a player.

Now, with this setup in each case I try 4 different things.

1. I can reset everything and get the information, that p was still in the scoreboard (and is not anymore afterwards).

   /scoreboard players reset *
   Reset scores of player p

   /scoreboard players test p o * *
   No o score for p found

   /scoreboard players reset *
   All matches failed

2. If I reset just the objective o then apparently the system realizes, that the player is completely reset.

   /scoreboard players reset * o
   Reset scores of player p

   /scoreboard players test p o * *
   No o score for p found

   /scoreboard players reset *
   All matches failed

3. If I instead remove the objective o then the scoreboard system doesn't fully realize that player p is gone. (Or rather should be gone.)

   /scoreboard objectives remove o
   Removed new objective 'o' successfully

   /scoreboard players test p o * *
   No objective was found by the name 'o'

   /scoreboard players reset * p
   No objective was found by the name 'o'
   All matches failed

   /scoreboard players reset *
   Reset scores of player p

   /scoreboard players reset *
   All matches failed

4. If I remove o and then recreate o then you see that p seems to still have a score o according to "/scoreboard players reset" but to have no score o according to "scoreboard players test".

   /scoreboard objectives remove o
   Removed objective 'o' successfully

   /scoreboard objectives add o dummy
   Added new objective 'o' successfully

   /scoreboard players test p o * *
   No o score for p found

   /scoreboard players reset * o
   Reset scores of player p

   /scoreboard players reset *
   All matches failed

In my opinion in cases 3. and 4. the game should reset the player's scoreboard entries for that objective properly when the objective gets removed.