(Comment converted into answer)
This section refers to nested try-catch blocks in general, i.e. not limited to the code sample verbatim.
In general, any function or pieces of code that performs multiple actions, and in which the error-handling / application state cleanup differs depending on which action / where in the code fails, the use of multiple try-catch blocks is necessary.
As other answers pointed out, the best coding style will extract these inner try-catch blocks into their own methods, and give these methods appropriate names that describe what they are "trying". In more complicated code, the method name should also become more wordy; they should describe what cleanup they are to perform.
This section refers to the code sample verbatim.
I suspect OP has a misunderstanding of how nested try-catch works.
When the innermost code block throws, it would be caught by the inner catch. To the extent that the inner catch block doesn't throw/rethrow, and doesn't inadvertently cause a different exception to be thrown, the outer catch will not catch anything.
Either the code sample is overly simplified - missing the
rethrow, or that something is omitted (or indeed missing in the original code) that hinders our understanding of the code that OP has in mind.
Thus, the meaning of the outer catch block will need to be studied (researched) carefully, to identify whether there's any possible (no matter how unlikely) circumstances that would trigger the outer catch.
This is a justified case of leaving comments in the code. Such analysis is often time-consuming, and it is far from obvious.
Also, the circumstances that lead to the outer catch being triggered may be rare enough (such that a typical programmer might not even be aware of such possibility), but may have occurred frequent enough to earn a place in the issue-tracker. A comment should point out this possibility by pointing to the issue-tracker ticket, so that a programmer can know how to re-create the situation, in order to test that future code changes will continue to handle this rare situation correctly.