Sometimes writing your thought helps...
Apparently something wasn't reporting correctly so far, but using the debug level, I finally end up getting some information. I should mention that the word that seems to provoke this issue is ' del ' (with two spaces around it). If those 3 letters are included in another word, nothing weird happens.

When the word is there on its own, though, this is my debug log (I have surrounded the most obvious issue with two blank lines):

2017/04/26 18:38:52 [debug] 6496#6496: *350 http keepalive handler
2017/04/26 18:38:52 [debug] 6496#6496: *350 malloc: 000055B18C6ADF30:1024
2017/04/26 18:38:52 [debug] 6496#6496: *350 recv: fd:16 978 of 1024
2017/04/26 18:38:52 [debug] 6496#6496: *350 reusable connection: 0
2017/04/26 18:38:52 [debug] 6496#6496: *350 posix_memalign: 000055B18C6C0F10:4096 @16
2017/04/26 18:38:52 [debug] 6496#6496: *350 http header: "Host: dev.www.myorg.edu"
2017/04/26 18:38:52 [debug] 6496#6496: *350 http header: "Connection: keep-alive"
2017/04/26 18:38:52 [debug] 6496#6496: *350 http header: "Content-Length: 16639"
2017/04/26 18:38:52 [debug] 6496#6496: *350 http header: "Pragma: no-cache"
2017/04/26 18:38:52 [debug] 6496#6496: *350 http header: "Cache-Control: no-cache"
2017/04/26 18:38:52 [debug] 6496#6496: *350 http header: "Origin: http://dev.www.myorg.edu"
2017/04/26 18:38:52 [debug] 6496#6496: *350 http header: "Upgrade-Insecure-Requests: 1"
2017/04/26 18:38:52 [debug] 6496#6496: *350 http header: "User-Agent: Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Ubuntu Chromium/57.0.2987.98 Chrome/57.0.2987.98 Safari/537.36"
2017/04/26 18:38:52 [debug] 6496#6496: *350 http header: "Content-Type: multipart/form-data; boundary=----WebKitFormBoundaryfufPzGfQx0XTvHjM"
2017/04/26 18:38:52 [debug] 6496#6496: *350 http header: "Accept: text/html,application/xhtml+xml,application/xml;q=0.9,image/webp,*/*;q=0.8"
2017/04/26 18:38:52 [debug] 6496#6496: *350 http header: "Referer: http://dev.www.myorg.edu/en/node/734/edit"
2017/04/26 18:38:52 [debug] 6496#6496: *350 http header: "Accept-Encoding: gzip, deflate"
2017/04/26 18:38:52 [debug] 6496#6496: *350 http header: "Accept-Language: en-US,en;q=0.8,es;q=0.6,fr-FR;q=0.4,fr;q=0.2"
2017/04/26 18:38:52 [debug] 6496#6496: *350 http header: "Cookie: DrupalModuleFilter=activeTab%3Dall; SESSb62f82f041805dbb55d5167522aaa24e=y-yFLoyVXBRCGSmicYphWW-OCVYIGphmDhmx9k9wubQ; SESSd452cfca8c0eccb9b5e4447bc1fa95dc=ENsFfcPE5jv4sTxlDxc40kg09aFMu7S-ZXJHPn0osb4; has_js=1; Drupal.tableDrag.showWeight=0"
2017/04/26 18:38:52 [debug] 6496#6496: *350 http header: "DNT: 1"
2017/04/26 18:38:52 [debug] 6496#6496: *350 http header done
2017/04/26 18:38:52 [debug] 6496#6496: *350 generic phase: 0
2017/04/26 18:38:52 [debug] 6496#6496: *350 rewrite phase: 1
2017/04/26 18:38:52 [debug] 6496#6496: *350 test location: "/"
2017/04/26 18:38:52 [debug] 6496#6496: *350 using configuration "/"
2017/04/26 18:38:52 [debug] 6496#6496: *350 http cl:16639 max:52428800
2017/04/26 18:38:52 [debug] 6496#6496: *350 rewrite phase: 3
2017/04/26 18:38:52 [debug] 6496#6496: *350 post rewrite phase: 4
2017/04/26 18:38:52 [debug] 6496#6496: *350 generic phase: 5
2017/04/26 18:38:52 [debug] 6496#6496: *350 generic phase: 6
2017/04/26 18:38:52 [debug] 6496#6496: *350 generic phase: 7
2017/04/26 18:38:52 [debug] 6496#6496: *350 access phase: 8
2017/04/26 18:38:52 [debug] 6496#6496: *350 access phase: 9
2017/04/26 18:38:52 [debug] 6496#6496: *350 access phase: 10
2017/04/26 18:38:52 [debug] 6496#6496: *350 access phase: 11
2017/04/26 18:38:52 [debug] 6496#6496: *350 post access phase: 12
2017/04/26 18:38:52 [debug] 6496#6496: *350 try files phase: 13
2017/04/26 18:38:52 [debug] 6496#6496: *350 http request body content length filter
2017/04/26 18:38:52 [debug] 6496#6496: *350 malloc: 000055B18C6F4100:8192
2017/04/26 18:38:52 [debug] 6496#6496: *350 http read client request body
2017/04/26 18:38:52 [debug] 6496#6496: *350 recv: fd:16 -1 of 8192

2017/04/26 18:38:52 [info] 6496#6496: *350 recv() failed (104: Connection reset by peer), client: 190.117.233.77, server: dev.www.myorg.edu, request: "POST /en/node/734/edit HTTP/1.1", host: "dev.www.myorg.edu", referrer: "http://dev.www.myorg.edu/en/node/734/edit"

2017/04/26 18:38:52 [debug] 6496#6496: *350 http client request body recv -1
2017/04/26 18:38:52 [debug] 6496#6496: *350 http finalize request: 400, "/en/node/734/edit?" a:1, c:1
2017/04/26 18:38:52 [debug] 6496#6496: *350 http terminate request count:1
2017/04/26 18:38:52 [debug] 6496#6496: *350 http terminate cleanup count:1 blk:0
2017/04/26 18:38:52 [debug] 6496#6496: *350 http posted request: "/en/node/734/edit?"
2017/04/26 18:38:52 [debug] 6496#6496: *350 http terminate handler count:1
2017/04/26 18:38:52 [debug] 6496#6496: *350 http request count:1 blk:0
2017/04/26 18:38:52 [debug] 6496#6496: *350 http close request
2017/04/26 18:38:52 [debug] 6496#6496: *350 http log handler
2017/04/26 18:38:52 [debug] 6496#6496: *350 free: 000055B18C6F4100
2017/04/26 18:38:52 [debug] 6496#6496: *350 free: 000055B18C6C0F10, unused: 128
2017/04/26 18:38:52 [debug] 6496#6496: *350 free: 000055B18C6F30F0, unused: 1648
2017/04/26 18:38:52 [debug] 6496#6496: *350 close http connection: 16
2017/04/26 18:38:52 [debug] 6496#6496: *350 reusable connection: 0
2017/04/26 18:38:52 [debug] 6496#6496: *350 free: 000055B18C6ADF30
2017/04/26 18:38:52 [debug] 6496#6496: *350 free: 000055B18C6AF150, unused: 112


So in my case I got a 104: Connection reset by peer. Usually, this error message is followed by "while reading response header from upstream", but that's not my case. It looks like the issue is only the connection between my browser and Nginx, and nothing more. This is confirmed by the fact that I don't get anything in my backend's access logs.

Is there anything else in this error log that should point me to a particular type of issue?