My futures trading coach (a professional trader) did that during the Japan's mother-of-all-mega-Tsunami. He earned tons of money despite the extremely massive margin requirement. But most traders have to top up their accounts. Good luck catching falling knives with bare hands.
Now now... due to the 'efficient market hypothesis', markets are efficient. Therefor, the price he gets for the puts will off-set the falling market
Ok what do you mean by "keep the stock"? You want to keep the short position or you want to buy the stock hence keeping the stock? You are shorting the stock but you are talking as if you are long the stock and thus wanting to "keep the stock" so I will assume that you want to keep the short position on the stock. Anyhow, ASSUMING that your prediction of the $400 level is correct, then you need to sell the put with the strike price below $400 cuz anything at or above $400, your stock will be bought back on assignment and you will no longer be short. So that way, hopefully the stock price will stay at or above $400, then your stock will be short and you will be making premiums writing the put but if the price ever drops below the strike on your short put, then you will still be assigned and your stock will be bought back and your short position will be closed. If the price ever rises above your short price of $500 and keeps going up, then you will be f'ed. That short put premium won't save you. Hope this helps.
Correction: then you need to sell the put with the strike price below $400 cuz anything at or below the strike on your short put, your stock will be bought back on assignment and you will no longer be short. Actually as long as the stock price stays above the strike on your short put, your stock will be short and you will be making premiums writing the put. Ideally, you should be buying calls to protect the short position so you won't get short squeezed but selling put is fine if you really want to get some income and recuperate some of the cost of buying the calls if you ever decide to buy some calls.