Maybe in these sorts of situations a bit of subtle "coaching" to influence them to attempt to fix the situation on their own before you agree to throw money at their problem. Guide them with questions to see if there is anything they could do first to help themselves, and keep bringing the focus back to what they themselves can do. Only after you have exhausted all your options, then I would offer money.
"Hey tungsten, I need money. Can you give me some?"
"Why do you need it?" <--note how you don't say right off the bat "sure!". You answer their question with your own question.
"...well, if you must know, I need to pay my car repair bill, and I'm broke."
"Ah, I see. Sounds tough and stressful." <--observe and name what kind of impact their lack of planning is having on them, and leave it there for them to react to. Don't commit to anything here.
"Yeah, it really sucks." <--there, they've agreed that it is stressful for them. You can use this later!
"Well, what have you tried to do so far to pay your bill?" <--basically, the idea is to refuse to throw money at the problem until they have at least demonstrated an attempt to help themselves. But you ask this in a kind, curious way, and usually people won't register this as a "rude" question, they will experience it as genuine caring.
"Well... nothing. I just don't have any money to pay it."
"I hear you. But do you have two ideas on how to solve this? I can help you brainstorm."
"Well, my only idea is to borrow money, which is why I'm asking you."
"Ah. But I'm sure you have overcome something like this before. What else could work?" <--encouraging!
"... Maybe... I could call the mechanic and ask for a payment plan."
"Awesome! I think that could help a lot. What else? A combo approach with a few different strategies might help you feel less stressed. Perhaps you have a way to free up some cash in your budget temporarily?"
*indignant* "Rude! Who asked you?"
"Sorry. It was a thought I had, that I thought could be helpful. What about my idea wouldn't work?"
*sputters* "I'm paycheck-to-paycheck as it is! Where would I possibly be able to cut $200? The notion is absurd!"
"I hear you. And I know $200 is a lot of money, its hard to squeeze water from a rock. But even a little bit helps. If you'd like, I could help you go over your budget."
"No thanks."
"Do you think that you might be surprised by expenses like this in the future? This bill might be tough, but I wonder if there is a way you could plan for these types of things so they aren't so stressful on you." <--very sympathetic here! You want to help them solve their problem and feel better! (but by them saving themselves, not you giving them money if at all possible)
*blank look* "I'm not sure. That sounds so abstract, and I don't know how I could possibly plan for that."
"Well, let's just assume that sometime in the future, you will need your car fixed again. How do you want that situation to go next time? What would make things easier for you that time around?"
etc etc
Basically, you know this person best. Try to guide them towards problem solving, and not dwelling too much on woe-is-me. Just keep redirecting back to positive, problem solving territory: "Well what have you tried?" "What else could you try?" "What about X?" "What would make this situation easier for you the next time it happens?" "What do you want to be different next time?"
But if you are close to this person and are happy to help out (as you say in your OP), then at the end, after exhausting the rest of the avenues and they are still coming up short, you can offer to cover the difference. But you really want to see them try to make progress on their own first, and you are helping them exercise their problem solving muscles so they can hopefully become more self-reliant. So even if at the end they are getting money, at least they will have gotten a bit of a mind exercise over how they can do this themselves next time.