Cross Sell detects if a product is unavailable and will instead display the next available assigned item.
We recommend assigning a few more items more than the max chosen to display. For example, if your settings are currently set to display 5 Cross Sell items max, you could increase the total assigned to say 7 or 8 with a few 'backups' to ensure that a display of 5 will be output at most times.
This functionality is currently active if you installed after 21st November 2015.
If you installed Cross Sell prior to 21st November 2015 and would like your Cross Sells to be Stock-aware, then please get in touch with us at firstname.lastname@example.org with the topic of 'Stock-aware' and we'll happily get that set-up for you.