Rules and Errata

The classic situation being Ablaze + Deadly, but there are other similar cases.

Ablaze: At the end of your turn, suffer 1d4-2 Fire damage.
Deadly: When you suffer damage, it is increased by 1.

If a 2 is rolled on the Ablaze d4, zero damage is suffered. Would Deadly increase that to 1? Or would Deadly not take effect? If zero counts as an amount of damage that can be suffered, "When you suffer damage" abilities would be activated. If zero damage equivalent to no damage, the "When you suffer damage" would not have occurred.
(And likewise for negative damage, if a 1 is rolled on the Ablaze d4.)

[There are similar questions with healing zero and shuffling zero. (For example, Leech with Sarenrae's Light, or pre-Core Ambush when the encountered monster is defeated and banished.) I think the answer would be the same, but these could be made into separate issues if it's better to consider each circumstance separately.]