Do emblems stay after the player dies?
Some effects put emblems into the command zone. An emblem is a marker used to represent an object that has one or more abilities, but no other characteristics. 113.2. An effect that creates an emblem is written “[Player] gets an emblem with [ability].” This means that [player] puts an emblem with [ability] into the command zone.
An emblem has no characteristics other than the abilities defined by the effect that created it. In particular, an emblem has no name, no types, no mana cost, and no color. 114.4. Abilities of emblems function in the command zone.
Debadging is not illegal, so there should be no reason for you to get pulled over or ticketed for it.
Emblems can’t be destroyed, as the “destroy” keyword only applies to permanents, and emblems are not permanents. R&D has no plans to create spells that are able to remove them. Emblems are a planeswalker-only thing.
Emblems have no color, name, card type, or other characteristics beyond the listed ability. The emblem is the source of the triggered ability. Because emblems are colorless, you can target permanents with protection from white or from blue, for example, with the triggered ability.
An emblem is not a permanent, and absolutely nothing can touch it or get rid of it as long as the player who gained it remains in the game, simply because no cards say that they can. Restarting the game eliminates all emblems, and subgames are unaffected by emblems in the main game.
There are currently no cards that explicitly remove emblems. The only way to get rid of an emblem is by activating the last loyalty ability on Karn Liberated. This restarts the game, and resets everything in the game except a specific set of cards that he keeps track of.
Emblems are not Legendary, nor are they permanents. They exist in the Command Zone. As of now, nothing in the game interacts with them in any way (other than the effects they have). You can create as many emblems as you wish.
Yes, they stack. For example, you can have multiple [[Sorin, Lord of Innistrad]] emblems and each one gives a separate power boost.
The emblem stays, because it is owned and controlled by the OP, not the player who “died”. Text on Ob Nixilis Reignited: “Target opponent gets an emblem with…”