Stonecoil Serpent with X = 0 + The Great Henge
The Serpent dies and you draw a card.
The timing is as follows:

The Serpent enters the battlefield with 0 counters. The Henge triggers.
State-based actions are checked and performed. The Serpent dies because it has zero toughness
The ability from the Henge (and anything else that triggered during point 1 and 2) is put on the stack.
You gain priority and can play instants and activate abilities. Then your opponent gains priority.
Eventually, the triggered ability from the Henge gets to resolve. It tries to put a +1/+1 counter on the serpent, but fails. It then instructs you to draw a card.

The first points can be deduced from rule 116.5:

116.5. Each time a player would get priority, the game first performs all applicable state-based actions
as a single event (see rule 704, “State-Based Actions”), then repeats this process until no state-based
actions are performed. Then triggered abilities are put on the stack (see rule 603, “Handling
Triggered Abilities”). These steps repeat in order until no further state-based actions are performed
and no abilities trigger. Then the player who would have received priority does so.

For point 5, consider the Gatherer ruling on the Henge:

Once The Great Henge’s last ability has triggered, you’ll draw a card even if you can’t put a +1/+1 counter on the creature for some reason (most likely because it has left the battlefield).

This originates from rule 609.3:

609.3. If an effect attempts to do something impossible, it does only as much as possible.

The Henge's ability tries to put a counter and the serpent and making you draw a card. It can't do this. It therefore does as much of it as they can, which is just making you draw a card.