If the stock no longer exists the option will be adjusted to make the underlying the same thing the person who owned 100 shares received for the stock. So if the shares are worthless, a put will be worth its intrinsic value. It would be helpful to be short shares, short calls or long puts if bankruptcy occurs
For whole stock splits, the number of contracts is increased and the strike price is reduced. For example, if XYZ splits 3:1, one July 60 put will become 3 July 20 puts.
For fractional stock splits, the number of shares covered per contract is increased and the strike price is reduced. For example, if XYZ splits 3:2, one July 60 put will become 1 July 40 put covering 150 shares.
For reverse splits, the number of shares covered per contract is decreased. For an example, see: