Losing newlines when reading from stdin - bash

Question

I have been beating my head up about this.
I wanted to loop over a multiline string character by character in bash but was loosing all newlines. First thing I did when i didn't find any obvious error was to run shellcheck on it, it seemed fine with the program.
script.sh:
#!/usr/bin/env bash
transform_single() {
if [[ $# -ne 1 ]]; then
echo 'Error: illegal number of args' 1>&2
fi
equation=''
delim0=0
delim="$1"
while IFS= read -rn1 c; do
if [[ $delim0 -eq 0 ]] && [[ "$c" == "$delim" ]]; then
delim0=1
equation=''
elif [[ $delim0 -ne 0 ]] && [[ "$c" == "$delim" ]]; then
delim0=0
echo -n "$equation" | texmath
elif [[ $delim0 -ne 0 ]]; then
equation="$equation$c"
else
echo -n "$c"
fi
done
}
transform_single '$'
input.txt:
<newlines>
<newlines>
# Hello world!
<newlines>
This is a test string.
<newlines>
invocation:
bash script.sh < input.txt
output:
# Hello world!This is a test string.
excepted output:
The same as in the input file.

Answer 1

Working script
#!/bin/bash
transform_single() {
if (($# != 1)); then echo 'Error: illegal number of args' 1>&2; fi
equation=''
delim0=0
delim="$1"
while IFS= read -r -d $'\0' -n 1 c; do
if ((delim0 == 0)) && [[ "$c" == "$delim" ]]; then
delim0=1
equation=''
elif ((delim0 != 0)) && [[ "$c" == "$delim" ]]; then
delim0=0
echo -n "$equation" | texmath
elif ((delim0 != 0)); then
equation="$equation$c"
else
echo -n "$c"
fi
done
}
transform_single '$'
The issue is that you must set a delimiter to read, a null character, to preserve line feed.