I’d suggest always assuming that a student is burdened. It’s not your job as an educator to diagnose someone’s situation, only to provide support and accommodation. And no matter how frustrated you might get, never act behaviorally as though a student is “irrevocable”. People pick up on it when people think they are hopeless, and it’s incredibly unempowering and demotivating. It’s okay to feel stuck or like you aren’t making progress with someone, those feelings are fine and normal, just make sure you always treat someone with respect, and the assumption that they are making the best decisions they can for what matters to them in life.
How do you motivate someone who does seem totally stuck? I think that’s an understandable question but the wrong one. You can’t change a person, you can’t make them feel new desires, you can’t fix all the burdens they are facing. But you can provide support, ask what they need, provide accommodations, be patient, and illustrate in your own actions why the tasks you’re asking them to do are worthwhile. They may some day want to use all the great support you have to offer. Or they might at least be thankful that you always treated them with dignity and autonomy as much as you could.