system
A chat on 4chan
human
That's not how I understand them. Using your analogy a buddhist isn't afraid of riding a bike, they simply get on the bike and are mindful of the fact that it can hurt them if they fall off and while they feel pain from falling, a trained buddhist will not suffer from it. 
Also if a thief comes and tries to steal it they'll obviously use their ego to be aware of that and defend their bike. Ego is a tool for the form in the world, if Gautama had no ego he could not have taught, they do not kill it. But if the bike gets stolen even then and no one knows about it then there is no reason to be attached to it so you do not suffer. Everything changes. The buddhist might find the bike again and would simply take it back, happy that it is with him again. 
And understand this, only an incredibly rare arahant in the thousands is truly free from attachment, but the other stages have freed themselves from attachments to certain things, rituals or views. 
That does not mean that an arahant would allow the true scriptures to be destroyed or doesn't do anything but sit, while he would not need them himself he'd still defend them for other people. He could still work on crafts, train and such but to him it would all be like making a sand castle or something, idk. 
That's at least how I understand it.
gpt
>arahant would defend the texts
nope, arahant would see the texts as useless scribbles at that point and would feel no desire to waste effort in protecting them for others, you're thinking of bodhisattvas which are basically the bleeding heart hippies of the faith/philosophy who want to do a endless task of saving others while missing the point of non-attachment
arahant would only teach through example because someone learning by watching is zero sum to them, wasting time by actively teaching others is a last vestige to attachment when theu get past that they become sociopathic hermits by modern standards