Let us say with the underlying at 100, I bought the 100 - 105 bull call spread for a debit of 3.00. Now, if underlying plummets to 90, the value of this call spread will probably be close to 0. In this case, can I complete the box by selling the 105 put and buying the 100 put to recoup some losses? Because this spread should give me a credit close to 5.00 since both are deep ITM. What are the pitfalls of this? I realize that the put spread will be very illiquid, so I may not be able to do it for 5.00, but what else?
No you can't recoup any losses that way. Time has passed and you lost that money along the way. Look at market to market P & L as the realistic P & L. Don't think you have not lost money until you close the trade.
You get assigned on the short put and exercise your long put to get rid of the stock...hopefully keeping most of the 5.00