In real life cops often try to arrest suspects/criminals rather than kill them for doing a crime. An arrest involves restraining the suspect, putting them in handcuffs, and taking them to the police station by cop car and so on and so forth for the criminal justice process. The slang term for being arrested is being "busted".
In Video Games
In games where the player can get arrested he/she is apprehended by the police when it happens. It can but may not always in involve the player being formally placed in fully modeled visible handcuffs. When the player is arrested the in game consequences range from game over to losing some money as a fine/bribe for breaking the law. Whatever the case in all cases the player is interrupted from continuing what they were currently doing in the game. Games that can involve the player getting arrested are often crime games and racing games in which the player is usually just stopped from driving their car in the latter. Grand Theft Auto is a famous series where this concept is present though it is not the first game with it.