Q:

What percentage of closed questions were reopened after an edit?

One of the assumptions Stack Exchange seems to operate on is that bad questions can be corrected and brought back to life.
Do we know what percentage of questions that were voted to be closed were subsequently reopened after an edit?

A:

Interesting question; all I can offer right now is this SEDE query which suggests a percentage of 14% on Stack Overflow and 8% on Meta Stack Exchange.

Some caveats:

SEDE does not include (enough) information about deleted posts. The worst closed questions get often deleted by Roomba, and it wouldn't surprise me if the real percentage is only half of this. It would be nice if one of the Stack Exchange employees could run the query on their own database (which does include deleted posts) but they have something on their hands which is about ten orders of magnitude more important right now.
This assumes the question is closed, not just voted to close - individual close votes aren't stored in SEDE.
It only looks at the timestamps of the event, it's impossible to determine if the edit itself was the reason to reopen the question. Maybe it would have been reopened without the edit.
It does not check if the question is subsequently closed again.
SEDE is updated once a week, on Sunday morning. That shouldn't be a real problem for analysis like this, though.

A:

I ran @Glorfindel's query against the GIS Stack Exchange and found that the re-open percentage there is 52%:

