My goal is to let user possibility to login using only password. There is any available plugin or module for that? I had a problem to find it.
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Content Password Plugin
The Content Password plugin worked well to password protect content on a Joomla page but unfortunately was not updated by the developer for newer versions of Joomla.
Fortunately, it looks like someone has resurrected the project for Joomla 3.x at: https://github.com/projoomexperts/Joomla-Content-Password-3
JLex Block from $29
JLex Block can "Set a password for any number of page or elements on page."
.htaccess/.htpasswd Password Protection
You may be able to password protect a Joomla page using .htaccess and .htpasswd. See https://stackoverflow.com/q/14603568/1983389 for some options.