Is it possible to create a rule on the event "after saving an existing block"? The reason of such a rule would be that there is just one block a certain user can edit. And when he does so, after saving he is redirected to the blocks management page, which he has not the permission to see and manage. So I wish there would be a rule that allows to redirect "after saving an existing block" (combined with a condition of a certain user) to some other page. 

I can't find any information about it in the documentation.
How is the user getting to the edit block screen? If its via contextual links then that should already be taking you can to the page you were on?

Or do you provide them the link to end the block? If so you could use the destination parameter to redirect then automatically (Same as what contextual links do) e.g.:

/admin/structure/block/manage/block/1/configure?destination=MYPAGETHEYSHOULDGOBACK