"Negate" vs. "Destroy" and Continuous Cards
Negating the activation of a card or effect and destroying that card are not the same thing; as such, even if a card is Chained to the activation of a card or effect to destroy that card, its effect may still resolve, with or without effect.
Chaining "Raigeki Break" to the activation of a monster effect such as that of "Number 11: Big Eye" will destroy the monster, but its effect will still resolve (so "Number 11: Big Eye" will still allow the player to take control of one of their opponent's monsters).
Spells and Traps
Chaining "Mystical Space Typhoon" or "Dust Tornado" to a Normal Spell, Normal Trap Card, Quick-Play Spell Card or Ritual Spell Card has no effect on gameplay, as it does not negate the card's effect. If such a card is activated and is destroyed by a card, its effect still resolves and the card used to destroy it is essentially wasted.
Field Spells, Continuous Spells and Continuous Traps
Continuous, Field, or Equip Spell Card, or Continuous Trap Card do not work in the same manner as other spells and traps. These cards need to remain face-up on the field in order to apply their continuous effects and their other effects that are activated on the field. If one of these is removed from the field after being activated but before its effect resolves, it still resolves but with no effect. However, other effects on these cards (such as separate Trigger-like effects) will still behave in their typical way.
If "Macro Cosmos" is activated, and your opponent Chains "Mystical Space Typhoon" to its activation, then "Macro Cosmos" is destroyed, and it resolves with no effect; you do not get to Special Summon a "Helios - The Primordial Sun". Similarly, if you activate "Fire Formation - Tenki" and it gets destroyed by "Mystical Space Typhoon" in the same Chain, you do not get to add a Beast-Warrior-Type Monster.
However, if you you were to activate "Mystical Space Typhoon" to target a face-down "Macro Cosmos", the "Macro Cosmos" could be activated and chained in response to Mystical Space Typhoon's activation. In this case, because the chain resolves backwards, "Macro Cosmos" would still be face up on the field when its effect to Special Summon "Helios - The Primordial Sun" resolves, and "Helios - The Primordial Sun" would be summoned before Mystical Space Typhoon's effect would destroy and remove "Macro Cosmos" from the field.
Note that Trigger-like effects are treated normally. For example, if "Geartown"'s activation is negated by "Magic Jammer", then its Trigger-like effect will resolve. However, there are a few edge cases. For example, if "Geartown" is activated as Chain Link 1 and "Mystical Space Typhoon" destroys it as Chain Link 2, the last thing to happen in this case would be Geartown resolving without effect; Geartown's resolution without effect didn't actually have any effect on the state of the game, but it nevertheless was not the last thing to happen and thus Geartown cannot activate its effect.
- Step 1: Player A activates "Raigeki".
- Step 2: Player B Chains "Imperial Order" to negate the effect of "Raigeki".
- Step 3: Player A Chains "Mystical Space Typhoon" to destroy "Imperial Order".
The Chain resolves in reverse:
- Step 3 resolves first. "Mystical Space Typhoon" destroys "Imperial Order".
- Step 2 resolves next. However, "Imperial Order" has been destroyed, so its effect is not applied.
- Step 1 resolves last. "Raigeki's" effect activates as normal.
For exactly the same reason, if you Chain "Mystical Space Typhoon" to "The Eye of Truth", "Future Fusion", "Premature Burial", or "Call of the Haunted", the effects from those cards resolve with no effect.