define fake liquidity

I'll have a go.

If orders are pulled the moment someone actually tries to match the market price, it's a clear indication the parties putting up the offers were not willing to accept the price they had put up.

I think that's fair. It would mean much less liquidity available though as your risk taking capability was reduced. Would traders actually be willing to accept the much thinner books if some kind of economic or regulatory enforcement of this was in effect? Maybe if they knew it was 'higher' quality liquidity and they could depend on it being there.

When an algo puts a bid in and pulls it quickly if the bids start getting hit. It makes the order book seem thick but if there is any decent order flow there is no liquidity to be found.