A Beloved Princess is a player who, upon death, causes the next Day phase to be skipped.
"Beloved" has also been seen as a role modifier that duplicates this effect.
Beloved roles are most often pro-Town. They are either seen in setups designed especially for them (so it is acceptable for their death to be a "punishment" for the Town) or in role madness games where skipping a Day phase is not a complete disaster.
Despite the name, Beloved is not a well-liked modifier in most contexts. It is seldom seen and possibly still overused.
A common variation for Beloved Princess is that the Day-skipping event only occurs if the Beloved player is lynched. If the Beloved player is killed in any other way, nothing special happens. This significantly increases the chance of the Beloved role not crippling the Town.
Use and Power
As mentioned before, Beloved players only show up in games designed around them or in role madness scenarios due to their ability to take away a Day away from the Town.
In games designed around them, there is generally some kind of safety net in the game linked to the Beloved role such that if the Beloved player dies, the Town deserves what they get. For instance, in the game in which Beloved Princess initially appeared there was a Guard role that knew who the Princess was and had a limited-shot ability to protect the Princess from kills. In addition, it was known in advance that the Princess and Guard were in the game. This sort of setup can make for an interesting Mafia variant; however, it is susceptible to being wrecked by bad play from the Guard or Princess.
In role madness games, a Beloved role simply serves to add emphasis to the impact of the game's Night actions. To that end, it increases the swing of the game even more. As it still punishes Town overall, it serves as a heavy-handed means of weakening the Town.