Let's say I write a covered call and a buy separate put option. After a period of time, the call expires, leaving me with the underlying stock. Thereafter, the market price went down and I can exercise my put option. Will the underlying stock that I own before be use for the assignment?
Owning 100 shares and selling a covered call to fund the purchase of a put is called a long stock collar. If the strikes are different, it is equivalent to a vertical spread. If they are of the same series, it's a conversion.
The only way that you could exercise your long put to sell the stock AFTER the short call has expired would be if the put expired at a later date than the short call.