How to find who deleted a line from a file in a SVN repository?

I would check the history of the file and try and quickly find a revision where that line is present, and then blame between HEAD and that revision.

If the file has gone through 100 revisions since inception then if you binary search through revisions looking for that line you shouldn't have to look at more than 10 different revisions.

This does what you need automatically, though not very fast because it doesn't use binary search as suggested above:

svn log FILE | egrep '^r[0-9]' | sed -e 's/ .*//' | while read rev; do echo $rev ; svn cat FILE -"$rev" | grep "case STRING" && break  ; done 

svn log --diff will identify deletes with "-" in column zero. Grep for "r" also so you can see the revision.

% svn log --diff src/fozbo.cpp -r22222:HEAD | grep -e '^r' -e '^-.*xyzzy'
r22222 | jruser | 2016-07-19 20:16:07 -0400 (Tue, 19 Jul 2016) | 1 line
-   else if ( password== "xyzzy") {

There is also svn log --search but that will only search the commit message.