I know this might sound a bit repetitive, but I wouldn’t worry too much about it. If a very young trainerless pokémon as rare as dratini appears before a human, there are two possible reasons for it. First, it was abandoned or lost as an egg. If this is the case, then its chances of survival are actually incredibly low. Second, it’s not a hatchling but rather a juvenile, which in some species’ cases are difficult to distinguish. However, the difference is extremely important; juveniles can survive on their own, whereas hatchlings cannot.
The driving reason behind both of these things is actually the same: most pokémon nests aren’t easy to find precisely because of human involvement. That is, while we aren’t technically predators for pokémon, it’s true that we do remove them from their natural habitat. Pokémon by instinct will make their nests hidden, inaccessible, or both precisely to protect their young until they’re ready to go out into the world on their own. While young pokémon won’t necessarily die if they leave their nests, they’re still vastly inexperienced and may not be able to stand up to predators or other pokémon without the watchful eyes of their parents, so it’s extremely rare for a pokémon that young to be on its own, without anyone to help it develop its skills enough to battle.
With that having been said, dratini nests are especially difficult for humans to reach. Part of this has to do with the fact that dratini are so few in numbers (and thus aren’t as bold as magikarp, for an off-hand example), and the other part is that dratini fry aren’t particularly strong. Unless your friend dove deep into very remote lakes and fought her way past a swarm of protective dratini or dragonair (or perhaps even dragonite), it’s likely she simply happened across a pool of slightly older, more independent dratini. If that’s the case, then her dratini will be fine in her care.
However, if, perhaps, the dratini she had caught was indeed a fry, it’s actually safer in her care than out in the wild, as the nest was apparently too exposed to be safe. It’s also worrying if only one dratini, dragonair, or dragonite (whatever the mother might have been) was on guard, as dratini form colonies of many nests clustered together and guarded by multiple dragons. It may be a good idea to contact a local pokémon ranger or other authority to check on the nest and see if there’s anything wrong.