Let's say that you're a Sorcerer under the effects of Hold Person, can you cast a spell without a material component with the Subtle Spell metamagic?
No, you cannot cast
The problem is not with movement or speech (ie. performing components), but that hold person subjects you to the paralyzed condition:
A paralyzed creature is incapacitated (see the condition) and can't move or speak. (PHB 290)
An incapacitated creature can't take actions or reactions. (PHB 290)
The victim is incapable of taking actions and thus cannot cast spells at all. Not even with a bonus action, as:
anything that deprives you of your ability to take actions also prevents you from taking a bonus action. (PHB 189)