It is not possible to run debugger on Chrome OS without using dev mode. Luckily, debugger uses network connection to communicate with the NaCl debug stub. This makes remote debugging possible with debugger running on a remote machine and NaCl application running on Chrome OS machine.
On chrome://flags page there are two flags related to NaCl debugging. We need to enable "Native Client GDB-based debugging" flag and switch "Restrict Native Client GDB-based debugging by pattern" to "Debug everything except secure shell" or "Debug only if URL manifest ends with debug.nmf" value. Changes on chrome://flags page require browser restart to take effect. Log out, close and open the lid to restart the browser. If they are set properly, secure shell extension should work, but NaCl application we are trying to debug should hang waiting for debugger to connect.
Once you launch your NaCl application now, the NaCl debug stub opens 4014 port on Chrome OS machine. This port is not accessible from outside, so we need to tunnel it through ssh connection to remote machine. There are two ways to do this.
The first way is to open new secure shell tab or window and add "-R port-number:localhost:4014" to "SSH Arguments" field before connecting to remote computer. Then you can use secure shell to launch NaCl debugger on that machine where you should use "target remote :port-number" command to connect to debug stub running on Chrome OS.
The second way is to use an existing secure shell tab or window. Press enter, ~, shift+c. This combination opens ssh-prompt where you can enter "-R port-number:localhost:4014" command. Pressing enter returns control to normal shell where you can launch NaCl debugger and use "target remote :port-number" command to connect to debug stub running on Chrome OS.
In both cases the port number can be any free port number on the remote machine above 1024 including 4014.