Either you could make the problem(s) they’re facing at the start impossible to solve. If you do this, make it so that they don’t have any options to fix the problem (such as a friend or relative with a life-ending medical condition, money problems, living in a war zone, etc.). Picking a problem where it’s hard even to reduce the suffering may help with what you’re aiming for.
The other ‘powerlessness’ option is to put them under ongoing distress so that anxiety or sadness or anger is constantly in the background of their life. This should be easy to combine with the above suggestion but has more to do with their perception of the problem. Feeling powerless may be very reasonable, but it is worth separating problem from perception of problem, because a character can simply be in denial of an unsolveable problem, or they may be defeatist about a solveable one.
Alternatively, if your character doesn’t know themselves very well yet (for example, if your original character is a teenager), you could make this more about their way of responding to problems and use their lack of life experience to get wiggle room to expand your range of possible responses. That might give you more flexibility about not picking a cliche ‘tragic backstory’. It’ll also help with character development because you’ll have a deeper idea of why they’re acting the way they are rather than just writing what they’re ‘doing’, if that makes sense.
Freezing or apathy are good responses if that’s what you’re aiming for. If your character’s likely to freeze and hope the threat passes over then they’re less likely to do anything to respond to the threat. Therefore the problem is likely to hang around and keep on being a problem – and it might even get worse. Examples of that could be something like a demanding teacher, a heavy workload at home, work or school, or a friend with a problem that’s way above your original character’s skill level (many teenagers (in fact, many people of any age) are stumped when a friend declares they’re depressed or shows signs of an eating disorder. Introducing a moral dilemma into the mix might help).
By contrast your OC could be incapacitated in other ways: feeling like they ‘have’ to obey or fawn over the person presenting the threat (like a tyrannical boss for instance), or having anger issues where the red mist tends to fall easily so if they feel threatened they lash out and only realise what they’ve done afterwards, once the damage is done. That could be something like rage learned from a parent with an addiction, or never having learned from their parents how to calm themselves down and then being faced with teasing at school).
I suppose it comes down to is, you could either pick an option where an external threat is the actual threat, or an option where your original character’s lack or misuse of resources is the problem.Whatever you go for, I hope you enjoy the journey.