live ball appeal?

[tzme415]

At what point did this cease to be a force and need to be appealed? Did it happen once R1 passed home? If this is true, does it also hold true for non-force situations? For example, R1 on 3B tags up legally on a fly ball and slides around the catcher to avoid the tag, but misses home on the way by....rather than going to tag R1 could the catcher touch home and appeal the missed base or is this only allowed as a dead-ball appeal? I should know this, but the nuance of the rule escapes me.