Chrome version 66.0.3359.139 (Official Build) (64-bit)
Chrome version 68.0.3425.0 (Official Build) canary (64-bit)
Chrome version 67.0.3396.40 (Official Build) beta (64-bit)
Chrome version 68.0.3423.2 (Official Build) dev (64-bit)
Mozilla Firefox version 52.7.4 (64-bit)
NVDA version 2018.1.1
JAWS version 2018.1804.26 ILM 
Windows Version 1709 (OS Build 16299.371)

The following is with NVDA specifically since JAWS behavior captured in  bug 838405 , unable to backspace or delete in Docs with JAWS 2018

Steps to repro: 
Launch NVDA
Open a Doc with screen reader support enabled and braille mode NOT enabled
type in the word "test"
put cursor is after the last letter, "t"
press backspace 
Expected: the t character is deleted and NVDA says "t"
Actual: t character is deleted, nothing is announced 
press backspace again 
Expected/actual: the s character is deleted, NVDA announces "s" 
Move the cursor to the left between the t and e 
Expected: press backspace, it deletes and says “t”; if you press delete, it deletes e and says “e” 
Actual: press delete key, e character is deleted but NVDA says nothing 

Differences: 

NVDA + braille mode IS enabled (same in Chrome Canary, Dev, Beta, Stable):  Everything reads as expected; backspace and delete keys work, NVDA reads deleted characters 


NVDA + Firefox braille support is NOT enabled:
Backspace and delete work as expected

NVDA + Firefox braille support IS enabled: 
Backspace: works as expected
Delete key has its own problems: 
Type “This is a test” 
Put cursor to the left of the first word, to the left of the t character
Press delete key
Expected: should say h
Press delete says i
Press delete should say space, instead says the rest of what’s on the line, in this case “is a test”