Well , in the first place i dont think that Bitcoin will fall down so much , its possible to drop to $ 5000k but to drop to 1000$? Small chances for that to happen. But if that's gonna happen , I have no idea if it's gonna recover from that drop , but like I saw until now Bitcoin is always recover after a big drop . Like now , bitcoin dropped from $ 19k to to 6000k and know it's begin to recover really fast , its already raised up to 12k . And my answer to your question is YES , bitcoin could recover from that 1000$
Well we said that bitcoin will not fall below $10K but it did. And then it falls even deeper at $5K-$6K range. So everything is possible. But I do hope that it won't get as low as $1K though.
But if ever it would happen, then this could be consider as a GOLDEN opportunity once more to stash and accumulate more bitcoin.
And its another work for us to work at that $12K barrier again. We have been in this predicament many times in the past and overcome it. And this mental barrier is no exceptions.
Yes, everything is possible, but it's not a good signal for Bitcoin. If Bitcoin drops too much it's a clear signal Bitcoin has lost too much strength, demand. Signal that people have left Bitcoin, and when an event like this happens, it's hard to have faith that the currency will rise again.
If BTC drops near $1000 I'm not sure if it would be a golden chance, as the price would probably stagnate and to invest hoping to make profit from the volatility would be very risky. But some people would keep using Bitcoin, not mainly as speculative investment, but as currency (also investing the BTCs in something else, but not expecting profit only from BTC's fluctuations in price).
The reason of why I think that bitcoin at $1000 will be a steal is because that price is not really justified, bitcoin did not had segwit activated, and will probably get the lightning network activated sometime in the future so to me the price needs to be higher not lower so if I were to see bitcoin at that price again I will buy it without even thinking about it.