For those of you interested here are the results for the question on cataloging board games.
I received 9 responses. 3 of the libraries have games for in house use or programs. I will give you a summary of the other responses.
1. Games signed out on a sheet of paper. They find duplicate games at rummage sales etc. to resupply missing pieces.
2. When cataloging they keep an inventory piece list on the inside of the box and put the pieces in zip top bags with the contents listed. They count pieces and either charge patron if it is an important part or 3-D print a replacement.