Let's take a look at some other games that use a hostage/prisoner system.
Swat 4 and All Points Bulletin had a system where you could use less then lethal weapons to down an opponent, and then handcuff them. The handcuffed player would be stuck in place, during which time a teammate could rescue them or they would de-spawn after 15-30 seconds. This method favors faster paced gameplay, as there is less downtime, but some incentive to do so.
Applying this to crowfall, a player or team of players could use special non-lethal weapons (Nets, clubs, saps, special abilities, sleep traps, what-have-you) that could render a player weakened to a state he could be captured. The main benefit of this is it takes the player out of the fight longer than killing him would. To provide some economic incentive, it would reduce the money earned by the captured player for their battle, and give it to the ones who captured him, or alternatively, the captured player would have a extended respawn timer (think 5 to 10 minutes) and they could choose to pay the "ransom" and respawn faster (Hard-coded mechanic that they pay a few based on their level or similar factors).
Such a method would be easier to code in, and easier to understand and use. But it does lack a bit of the cool factor of "real" hostage taking.
A more "historical" method for Crowfall would be like this,
1. Hostage taking is limited to certain world rule sets, so on the easier ones, there is no hostage taking, on the harder ones, you can take anyone hostage.
2. It would take a group of players using special non-lethal weapons/skills/magic to down a player, during which time, a special item, skill, or ability is needed to "capture" them. Think of using manacles or a spell of binding. This item/ability isn't just physical, in lore terms, it prevents the hero from returning to his eternal kingdom.
3. The Captured player has a timer of 10 minutes, during which time, the group of players capturing him, much transport him to a magic prison, as the magic manacles/spell will wear off after that time, and the prisoner will be transported back to safety instantly (To prevent release/recapture abuse). During this time, other players may release the captured player if they get close enough or do a special action.
4. Once safely transported to a prison. The prisoner is locked into a dungeon in-game. The players who captured the prisoner must issue a ransom demand to the prisoner and/or their guild at the time of imprisonment. The ransom is either hard coded to set values based on level/skill, or has a variable cap based on those factors (So no setting a 99 billion gold ransom on level 1 players).
5. If the ransom is paid, the player is instantly transported to safety (Ransom demands could include whether the prisoner retains his/her items or not). If the ransom is not paid, the prisoner must remain in the dungeon for a period of time (1 hour in-game, or 12 hours if not logged in). During this time, the players who captured the prisoner may visit him, humiliate him (Allows for hilarious screenshots or humiliation for taunting players), release him, torture him, or execute him. Execution would carry specific penalties greater than normal death, as it represents weakening whatever powers that fuels that player's ties to the game world (hour or more debuff that persists, or the player is unable to enter that game world for a period of time).
It is important to note, that no method of keeping a player constantly in prison should exist, nor should being a prisoner last too long. There is also the alternative option that when a player is captured, it represents part of his characters life force/soul/spirit is simply captured, and is greatly weakened until the ransom is met or timer expires. This gives them the choice to keep playing or even attempt a rescue.