It is the same as what's described for the `set' builtin.

"All of the single-character shell options documented in the
 description of the set builtin command, including -o, can be
 used as options when the  shell  is invoked."

-e      Exit  immediately  if a pipeline (which may consist of a
        single simple command), a list, or  a  compound  command
        (see SHELL GRAMMAR above), exits with a non-zero status.
        The shell does not exit if the  command  that  fails  is
        part  of  the command list immediately following a while
        or until keyword, part of the test following the  if  or
        elif  reserved  words, part of any command executed in a
        && or || list except the command following the final  &&
        or ||, any command in a pipeline but the last, or if the
        command's return value is being inverted with !.   If  a
        compound  command  other  than a subshell returns a non-
        zero status because a command failed while -e was  being
        ignored,  the  shell  does  not exit.  A trap on ERR, if
        set, is executed before the shell  exits.   This  option
        applies to the shell environment and each subshell envi-
        ronment separately (see  COMMAND  EXECUTION  ENVIRONMENT
        above), and may cause subshells to exit before executing
        all the commands in the subshell.

        If a compound command or shell function  executes  in  a
        context  where -e is being ignored, none of the commands
        executed within the compound command  or  function  body
        will  be  affected  by the -e setting, even if -e is set
        and a command returns a failure status.  If  a  compound
        command  or  shell function sets -e while executing in a
        context where -e is ignored, that setting will not  have
        any  effect  until  the  compound command or the command
        containing the function call completes.

I can't reproduce this using bash-4.4, bash-5.0, or bash-5.1-alpha on macOS or RHEL 7.

Subject: read command terminating silently upon reading from heredoc

Configuration Information [Automatically generated, do not change]:
Machine: x86_64
OS: linux-gnu
Compiler: gcc
Compilation CFLAGS: -O2 -g -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -fexceptions -fstack-protector-strong -grecord-gcc-switches -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -Wno-parentheses -Wno-format-security
uname output: Linux fedoraminimalm13 5.7.8-200.fc32.x86_64 #1 SMP Thu Jul 9 14:34:51 UTC 2020 x86_64 x86_64 x86_64 GNU/Linux
Machine Type: x86_64-redhat-linux-gnu

Bash Version: 5.0
Patch Level: 17
Release Status: release

Description:
Copy/Paste the following lines (between triple) quotes to inside shell scripts a1.sh, a2,sh, a3.sh, a4.sh
```
define(){ IFS='\n' read -r -d '' ${1} || true; }
define VAR1 <<'ENDT'
 abc'asdf"
$(dont-execute-this)

foo"bar"''
ENDT
printf "AAR1\n${VAR1}BAR1\n"

{
IFS='\n' read -r -d '' VAR2 << 'ENDT'
 abc'asdf"
$(dont-execute-this)

foo"bar"''
ENDT
} || true ;
printf "AAR2\n${VAR2}BAR2\n"

IFS='\n' read -r -d '' VAR3 << 'ENDT'
 abc'asdf"
$(dont-execute-this)

foo"bar"''
ENDT
printf "AAR3\n${VAR3}BAR3\n"

IFS='\n' read -r -d '' VAR4 <<<'abc'"'"'asdf"'"\n"'$(dont-execute-this)'"\n\n"'foo"bar"'"''\n" ; printf "AAR4\n${VAR4}BAR4\n"
```
All 4 examples work on the command line
The last two examples do not work inside a script.
It is not clean what the "{} || true" have to do with making the read command work
# rpm -qa | grep bash-5
bash-5.0.17-1.fc32.x86_64

Repeat-By:
If typed directly in interactive shell mode, all 4 scriptlets work as expected.
However, when each script is run in batch infocation mode, a3.sh and a4.sh do not get to the subsequent printf statement and show output
Batch script terminates at read silently.
If the "{} || true is required for some reason", then that behavior is not documented in the man page 'read [' section
The effect is same in
- win10 -> Wezterm -> ssh-8.1 -> sshd8.3 -> bash GNU bash, version 4.4.23(1)-release (x86_64-pc-msys)
- win10 -> git-bash-mintty -> bash GNU bash, version 4.4.23(1)-release (x86_64-pc-msys)
- win10 -> pwsh-7.0.3 -> bash GNU bash, version 4.4.23(1)-release (x86_64-pc-msys)
- win10 -> VirtualBox-VM-Linux -> Fedora-32 -> console-tty -> bash GNU bash, version 5.0.17(1)-release (x86_64-redhat-linux-gnu)
- win10 -> Wezterm -> pwsh-7.0.3 -> bash GNU bash, version 5.0.17(1)-release (x86_64-redhat-linux-gnu)
- win10 -> hyperjs -> pwsh-7.0.3 -> bash GNU bash, version 5.0.17(1)-release (x86_64-redhat-linux-gnu)

Fix:
Basically, the intent was to raw read a heredoc inside a shell script.
Workaround: For that purpose just use the "{} || true" to make the read heredoc work as expected.