If you are running Linux Mint, and are installing from the Software Manager, there is no password required.
This has caused a few problems because some of the flatpaks have not been verified....in some cases the person responsible for assembling the flatpak has not been named. Usually there will be a sentence on the page saying (in this case for Google Chrome browser)...."
NOTE: This wrapper is not verified by, affiliated with, or supported by Google.
....and nothing else.
This has applied up until LM 21.3
From LM 22 this will not be the case.
Better security
In a blog post, the Linux Mint team explained why unverified Flatpaks represented a very important security issue:
https://blog.linuxmint.com/?p=4675
The post highlighted the fact that users REALLY need to trust where they get their software from, and that for most unverified Flatpaks, building up that trust is not possible.
Verified Flatpaks now show their maintainer name.
Unverified Flatpaks are disabled by default.
A warning reminds you of the security risks associated with them.
Unverified Flatpaks are disabled by default
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I realise your question may have meant....can the situation be bought about whereby a password
must be used to install a flatpak.
I think not. I have not encountered that possibility.