If LiveAgent is causing errors when you receive a Facebook message or email containing UTF8 emoji (emoticon, smiley) characters, it is caused by the database "collation" or "character set".
MySQL "utf8" only supported characters 3-bytes long. Emoji characters belong to the group of characters that occupy 4 bytes. To overcome this limitation MySQL introduced a fixed character set called "utf8mb4" in version MySQL 5.5.
If you install LiveAgent on database MySQL 5.5 or higher, the columns are already created with the correct "utf8mb4" character set. However, if you installed LiveAgent on database version MySQL 5.4 or older, the tables and columns were created with the character set "utf8". The tables and columns are not automatically converted even when you later update to MySQL 5.5 or higher. This conversion must be done manually.
To rectify this problem, you will need to open files /install/db/gpf/create.sql and /install/db/la/create.sql and search for string "utf8mb4" and then change collation and character set of the corresponding columns in your database.
Do not convert all collumns character sets to utf8mb4.