I think encryption can be one. If you don't know the internals and handle it as a black box, you can lose security. For example if you encrypt a string twice with a one time pad, you get back the original.
Another could be presenting content. For example saving content as html or pdf. Pdf has a concept of pages and you may have aesthetically suboptimal pagination if you try to abstract away the final format. You may even need to cut a sentence from the content to have optimal visuals.
Or if you tried to consider all image formats equally and autosaved to JPEG every minute while editing, the lossy compression would degrade quality.
The fix is usually exposing the particular aspect on the interface. The problem is that usually new things that we think should fit some abstraction turn out to have peculiarities we didn't think of when designing the abstraction. We thought our abstraction is more general and future-proof than it is.
A classic trap for new players is that in most modern compiled languages you can add strings and get a string, but strings are in fact immutable and can't be added without making an entirely new string and disposing of the original two. This means "a" + "b" is actually a horrible way to build up a string if you have to do lots of little additions, so most languages have some other method of making a string of strings/chars (StringBuilder in Java and C#, strings.Builder in Go, etc).
It's variant called rewrite rules is used in Haskell's compiler for ages and is a heart of good vector algorithms (on par with C, including SIMD C).
I can't find a paper I read in 1998 or so where successive calls to fputc were replaced with fputs and with some other rules and same approach the OpenGL code was optimized to be as fast as possible.
It is pity that research that is twenty years old was not put into C# compiler.
And for a bonus, look at program distillation: http://meta2012.pereslavl.ru/papers/2012_Jones_Hamilton__Sup...
They transform quadratic concatenation algorithm (O(n^2)) into linear one (O(n)).
In my mind, I add two strings like so:
https://gist.github.com/seisvelas/c11d200d0040a3686e47af0068...
That is, I realloc the first string to fit the second inside of it, then add the second string into the new space. But I have no idea what I'm doing. I'm posting this comment so someone can explain to me why my way is bad and why I should be creating a new string to put the others inside (which apparently is what everyone else does!)
Also for mutable strings you either have to allocate enough memory to fit the final result or have some kind of rope data structure. Or else you end up copying it anyway.