Alice is holding a security that is decreasing in value, and her book order isn't going to clear.

Assuming no HFTs, maybe Alice could set min_price=9.9$, and still sell for $10.05 in the better scenario? It seems that HFT's kill alice's sell spread option, forcing her to sell at min_price?

Huh? If Alice places a limit sell at $9.90, Bob's limit buy at $10.05 order will execute at $9.90. The limit price of the standing order is the one that prices the trade.

Oh, thanks for correcting my misunderstanding. So in general, sell "min_price" really just means sell "price"? Or are there circumstances that it would sell above that price?

As explained above, if Bob's $10.05 buy order was in the order book first, then Alice's $9.90 sell order would trade with Bob's buy order at $10.05.