As a general rule, people do not give dollars for nothing. It would be hard to expect the other person to accept this donation and believe that there are no strings attached. Its simply atypical. Accordingly, the answer would have to be "you can donate $2000 to someone if your particular relationship supports rising above this default assumption that there are strings attached."
The reason for this is that one of the purposes of money is to be usable for any purpose, not just the intended purpose. If I give you $100 to repair your car, and you buy concert tickets with it, I'll be angry. Accordingly in most environments, if I give you $100, I expect a certain level of transparency from you such that I can prove my $100 went to the right place.
Quite often the workaround is to directly support their needs, rather than giving them money. If they have $150 in rent due, instead of donating $150 to them, pay their rent directly. If they need car maintenance, pay the shop directly. In my cultural context (USA), this is much better etiquette. It also demonstrates that you're paying attention to them and their actual needs, rather than throwing money at them in the way one would throw money at a problem to make it go away.
Sometimes you can even do this anonymously, if you like. If you talk with a landlord, I expect you could pay rent anonymously for someone. The landlord just cares that they get paid.
There are counter examples, of course. Your relationships can vary. One personal anecdote from my life came from my fraternity, and a loan. When I was pledging, they had an event where the brothers tried their best to convey what "being a brother" meant to them. One of my brothers (we'll call him Alex) had a story that stuck with me. He needed $200 to help pay for tuition, or he was going to get kicked out of school. He was lamenting this when one of his fellow brothers (we'll call him Bob) came by. Bob didn't hear the whole story, just that Alex needed money. Bob just looked Alex in the eye and said, "You need money?"
"Yeah man, I need....", and Bob cut him off right there.
"How much do you need?"
And at that, Bob opened his wallet, handed Alex $200 and said "Pay me back whenever you can." Never asked what the money was for, when it would be paid back, or even if it could be paid back.
Now an open-ended loan like this isn't quite a donation, but it's darn close. I'd give this as an example of a particular relationship which permitted a gift of money with no strings attached. Indeed, Alex told us this story specifically to point out how unusual the relationship was between brothers at the fraternity. Usually interactions like that aren't done. But sometimes one can do so.