echo '$HOME'
$HOME

echo "$HOME"
/home/user

func '~/PATH_TO_FILE/FILE' - error
func '/home/$USER/PATH_TO_FILE/FILE' - OK

#!/bin/sh
clear; set -e

func()
{
echo "ARG1 = $1"
cd    $1
pwd
}

LST=01.lst

while read LINE
do
echo "LINE = $LINE"

ARG=$(echo $LINE | cut -d ' ' -f1)
ARG=${ARG// /}
func $ARG
done < $LST

~/tmp  sss

LINE = ~/tmp  sss
ARG1 = ~/tmp
./run.sh: line 7: cd: ~/tmp: No such file or directory

set expand-tilde on

expand-tilde

If set to ‘on’, tilde expansion is performed when Readline attempts word completion. The default is ‘off’.

#!/bin/sh
clear; set -e
set expand-tilde on

run.sh,  01.lst, вывод

#!/bin/sh
func()
{
  script=$(basename "$1")
  SCRIPT_DIR=$(dirname  "$1")

echo -e "$1\n$SCRIPT_DIR"
echo $PWD
cd "${SCRIPT_DIR}"
echo $PWD
}
func ~/123456

./scr.sh 
/home/konstantin/123456
/home/konstantin
/tmp
/home/konstantin

ARG=$(echo $LINE | cut -d ' ' -f1)

while read LINE

~> cat tilde-problem.sh
#!/bin/bash

f() {
    local var=$1
    var=${var/#\~\//$HOME\/}  # sed ~/path-like
    var=${var/#\~/$HOME\/}    # sed ~User-like
    echo "$1 ---> $var"
}

f ~/dev

f "~/quoted"

ARG="~/argquote"
f $ARG

ARG=$(echo -n "~/echoed")
f $ARG

f "~user"

#!/bin/bash
clear
# doesn't matter??
set expand-tilde off

f()
{
path=${null:$1}  # tilde hack
cd $path || exit 1
echo "
ARG[1]     = $1
PATH_HACK  = $path
PWD        = `pwd`
"
}

echo -n "### Test 1"
f ~/dev

echo -n "### Test 2 - should fail"
f "~/dev/"

echo -n "### Test 3 - should fail"
ARG="~/dev"
f $ARG

echo -n "### Test 4"
ARG=$(echo -n "~/dev")
f $ARG

### Test 1
ARG[1]     = /home/sun/dev
PATH_HACK  =
PWD        = /home/sun

### Test 2 - should fail
ARG[1]     = ~/dev/
PATH_HACK  =
PWD        = /home/sun

### Test 3 - should fail
ARG[1]     = ~/dev
PATH_HACK  =
PWD        = /home/sun

### Test 4
ARG[1]     = ~/dev
PATH_HACK  =
PWD        = /home/sun

SCRIPT_DIR=`echo ${SCRIPT_DIR/\~/$HOME}`