It was not that easy (advanced Bash programming) and took some time, but I’ve got Bash auto-completion working on Linux Mint 19.1. I guess it will also work on other Linux distributions.
For the ones interested, do the following (with <tab> = pressing ‘tab’-keyboard key):
$ safe cat safe://acompl/safe_completion.sh > ~/.safe_completion.sh
$ source ~/.safe_completion.sh
$ safe <tab><tab>
$ safe ca<tab> s<tab>dweb/<tab>
$ ...
If you want the safe tab completion persistent: add
source ~/.safe_completion.sh
to e.g. ~/.bashrc
You can get .safe_completion.sh also from Github.
Of course you can change or improve this if necessary.