Note: This is a historical reference, not a current security baseline. Magento 1 is end-of-life.

The following error is printed on Magento upgrade via Connect Manager or ./mage CLI tool:

upgrade-all: Package community/Lib_Varien 1.9.4.5 depends on PHP extensions: Array

Cause

Most likely, mcrypt extension is missing in your PHP stack. You can get list of all installed PHP extensions on your server with php -m CLI command or get_loaded_extensions() function:
$ php -r "print_r(get_loaded_extensions());"
$ php -m
The list of all dependencies for Lib_Varien is defined in package.xml file of this package:

  
    
      5.4.0
      7.2.99
    
    
      Lib_ZF
      community
      1.12.10.21
      1.12.10.21
    
    
      PDO
    
    
      SPL
    
    
      curl
    
    
      SimpleXML
    
    
      dom
    
    
      gd
    
    
      iconv
    
    
      pdo_mysql
    
    
      mcrypt
    
    
      pcre
    
    
      Reflection
    
    
      session
    
  

Solution

You can find which PHP extension is missing in your case with something like the following:
(output=$(php -m); for extension in PDO SPL curl SimpleXML dom gd iconv pdo_mysql mcrypt pcre Reflection session; do echo -e "$output" | grep -q "^$extension" || echo $extension; done)
and install all required extensions with phpenmod command. For mcrypt extension it will take a bit longer as for PHP 7.2 the extension is in PECL repository and should be installed as a PECL package.