Some monsters have an Action/Legendary Action that allows them to teleport 120 feet. Using the Balor as an example:
Teleport. The balor magically teleports, along with any equipment it is wearing or carrying, up to 120 feet to an unoccupied space it can see.
Could it grab an enemy and then teleport them both 120 feet away?
How else are you supposed to know you can bring someone along? To put it another way, everything you need to know about Balor's teleport feature is contained in its description.
Consider the spell thunder step:
You can also teleport one willing creature of your size or smaller who is carrying gear up to its carrying capacity.
Thunder step explicitly states that you can bring a friend along. Since Balor's feature doesn't say another creature may come along, Balor's teleport feature is a solo trip (since other creatures are definitively not equipment).
But only in the specific case quoted.
There is no general rule on whether you can teleport with others and in what circumstances: some allow it, some don’t.
This one doesn’t. It explicitly says “The balor” and “any equipment it is wearing or carrying”. Another creature is not “equipment”.
Other abilities with different wording will have different results.
No, as a general rule.
Teleport powers are one person, with equipment, and cannot carry other creatures unless specifically stated. Some do specify that, such as Dimension Door that allows you to bring someone with you, or Thunder Step. The Teleport spell lets you bring others along. But any such spell or power that does not say you can carry others with you does not allow that.
First, spells and abilities can generally only do what they say. I've already seen the comments about how some argue about other spells leaving the teleporter naked, where I'd just call that a rule oversight. It is reasonable to assume that, unless otherwise stated in the rules, a character's effects would travel with them, regardless of the mode of transportation.
There's a lot of rules that we just assume. There are no rules about what kind of nutrition a creature must eat, just that they must eat. There's no rule that says that a dropped object falls to the ground, but we take it for granted it does, short of magical items like an Unmovable Rod. The rules are meant to lean heavily on common sense.
That said, if a spell or ability allowed additional targets, it'd definitely call it out in the spell text. For example, see Teleport, where you can transport up to eight willing creatures of your choice. It even goes further to say you can't target an object held by an unwilling creature.
Second, you can't generally use a spell or ability on an enemy without some sort of opposed roll or ability check, unless a rule specifically says otherwise. Any spell or spell-like ability that has any potential to affect additional targets will state what conditions must be met to affect those additional targets. If the Balor could relocate unwilling victims, there'd have to be a corresponding check, and it would be called out, or a specific exemption from this general rule.
I generally agree that there's some wiggle room for interpretation of some spells and other rules, but an important aspect here is that a player's agency shouldn't be violated without at least a chance to fight back. If I were to allow this to happen, there'd be at least a grapple check to have the Balor grab the target, and then (likely) a Wis save to resist the ability.
Without any rules to fairly arbitrate player agency, it wouldn't make sense to just let the Balor have their way, which could include things like teleporting up 120 feet with a victim, grabbing on to a ledge, then letting go, doing substantial damage in the process, all with no chance to save or avoid the damage.
I'd also say that this would become overpowered in the Balor's favor, allowing them to kill far easier than simple melee attacks. After all, that's up to 12d6 damage you can inflict every other turn while the characters helplessly splat on the ground. The players would have far more than a Challenge 19 on their hands at that point. Besides, Balors are already quite challenging to kill without having a cheap tactic like that at their disposal.
A passenger of any sort does not count as gear or equipment, so therefore the Balor would not be able to teleport along with an enemy.
