You would read directly from the file without the pipeline. This avoids running the while loop in a subshell, which allows you to see the changed value of $SOMEVALUE after the loop.

SOMEVAR="original value"

while IFS= read -r SINGLELINE
do
    SOMEVAR="updated value"
    printf 'this is a single line: %s\n' "$SINGLELINE"
    printf 'SOMEVAR is now: %s\n' "$SOMEVAR"
done <"$SOMEFILE"

printf 'Final SOMEVAR is: %s\n' "$SOMEVAR"

If you insist on having your $MULTILINE variable, then write that to a file and read it from there:

tmpfile=$(mktemp)
printf '%s\n' "$MULTILINE" >"$tmpfile"

while ...; do
   ...
done <"$tmpfile"
rm "$tmpfile"

Also related:

• Why is my variable local in one 'while read' loop, but not in another seemingly similar loop?

An answer to the above linked question also suggests writing your program in such a way that all uses of $SOMEVAR occurs within the subshell at the end of the pipeline:

MULTILINE=$(cat "$SOMEFILE")
SOMEVAR="original value"

printf '%s\n' "$MULTILINE" | {
    while IFS= read -r SINGLELINE
    do
        SOMEVAR="updated value"
        printf 'this is a single line: %s\n' "$SINGLELINE"
        printf 'SOMEVAR is now: %s\n' "$SOMEVAR"
    done

    printf 'Final SOMEVAR is: %s\n' "$SOMEVAR"
}

You would read directly from the file without the pipeline. This avoids running the while loop in a subshell, which allows you to see the changed value of $SOMEVALUE after the loop.

SOMEVAR="original value"

while IFS= read -r SINGLELINE
do
    SOMEVAR="updated value"
    printf 'this is a single line: %s\n' "$SINGLELINE"
    printf 'SOMEVAR is now: %s\n' "$SOMEVAR"
done <"$SOMEFILE"

printf 'Final SOMEVAR is: %s\n' "$SOMEVAR"

If you insist on having your $MULTILINE variable, then write that to a file and read it from there:

tmpfile=$(mktemp)
printf '%s\n' "$MULTILINE" >"$tmpfile"

while ...; do
   ...
done <"$tmpfile"
rm "$tmpfile"

Also related:

• Why is my variable local in one 'while read' loop, but not in another seemingly similar loop?

An answer to the above linked question also suggests writing your program in such a way that all uses of $SOMEVAR occurs within the subshell at the end of the pipeline:

MULTILINE=$(cat "$SOMEFILE")
SOMEVAR="original value"

printf '%s\n' "$MULTILINE" | {
    while IFS= read -r SINGLELINE
    do
        SOMEVAR="updated value"
        printf 'this is a single line: %s\n' "$SINGLELINE"
        printf 'SOMEVAR is now: %s\n' "$SOMEVAR"
    done

    printf 'Final SOMEVAR is: %s\n' "$SOMEVAR"
}

Also possibly related:

• Why is using a shell loop to process text considered bad practice?

Other questions that may be of interest:

• Why is printf better than echo?
• Are there naming conventions for variables in shell scripts?

You would read directly from the file without the pipeline. This avoids running the while loop in a subshell, which allows you to see the changed value of $SOMEVALUE after the loop.

SOMEVAR="original value"

while IFS= read -r SINGLELINE
do
 SOMEVAR="updated value"
 printf 'this is a single line: %s\n' "$SINGLELINE"
 printf 'SOMEVAR is now: %s\n' "$SOMEVAR"
done <"$SOMEFILE"

printf 'Final SOMEVAR is: %s\n' "$SOMEVAR"

If you insist on having your $MULTILINE variable, then write that to a file and read it from there:

tmpfile=$(mktemp)
printf '%s\n' "$MULTILINE" >"$tmpfile"

while ...; do
   ...
done <"$tmpfile"
rm "$tmpfile"

You would read directly from the file without the pipeline. This avoids running the while loop in a subshell, which allows you to see the changed value of $SOMEVALUE after the loop.

SOMEVAR="original value"

while IFS= read -r SINGLELINE
do
    SOMEVAR="updated value"
    printf 'this is a single line: %s\n' "$SINGLELINE"
    printf 'SOMEVAR is now: %s\n' "$SOMEVAR"
done <"$SOMEFILE"

printf 'Final SOMEVAR is: %s\n' "$SOMEVAR"

If you insist on having your $MULTILINE variable, then write that to a file and read it from there:

tmpfile=$(mktemp)
printf '%s\n' "$MULTILINE" >"$tmpfile"

while ...; do
   ...
done <"$tmpfile"
rm "$tmpfile"

Also related:

• Why is my variable local in one 'while read' loop, but not in another seemingly similar loop?

An answer to the above linked question also suggests writing your program in such a way that all uses of $SOMEVAR occurs within the subshell at the end of the pipeline:

MULTILINE=$(cat "$SOMEFILE")
SOMEVAR="original value"

printf '%s\n' "$MULTILINE" | {
    while IFS= read -r SINGLELINE
    do
        SOMEVAR="updated value"
        printf 'this is a single line: %s\n' "$SINGLELINE"
        printf 'SOMEVAR is now: %s\n' "$SOMEVAR"
    done

    printf 'Final SOMEVAR is: %s\n' "$SOMEVAR"
}