We get them too, mostly I just burst out laughing and yell "tell em ther'e dreaming" (or words to that effect) at the screen.

Then I walk away and go and water the garden or make a coffee etc etc........

After calming down, I come back and send off a polite reply with a price that we would accept and so leave it up to them to come back.

Sometimes they do, and then I will go in and change the listing to accomodate.  

We view low offers as the buyer trying to suss out our lowest price that we would accept, so quite often they do turn into sales. I usually just ignore the ridiculous offer, thank them for their interest and then advise our terms/price.

Find that if you are polite and courteous usually no problem, if they do send through some info we accept with good grace and thank them, check it out, then advise what you can/will do for them. If they have gone to that much trouble they obviously have a big interest in the item. 

Very hard sometimes to not be offended but they don't know your circumstances, and are only trying to "do a deal", and yes some people are very "cheeky".

But you are the one in control not them, and you don't have to sell to them if they are really obnoxious so would back you up there for sure. 

Up to you how you proceed.

Best Wishes.