the family variables are just a way to input the same variable into a bunch of instances without having to do it one by one. it also lets you manage those instances as a groups when needed. https://www.scirra.com/manual/142/families
however, as with all instances, their existence starts and ends with the layout. the only way to have permanent variables is by using Global Variables https://www.scirra.com/manual/83/variables
You could, however, store the instance variable, for later use, in a number of ways: You could use arrays, dictionaries, webstorage or global variables with numbers or even in JSON format to move the data from one layout into the next. (https://www.scirra.com/manual/108/array, https://www.scirra.com/manual/140/dictionary, https://www.scirra.com/manual/140/dictionary)
take your time to review the manual entries =)