All ice is encountered with its strength lowered by 1.
In the public consciousness, there's a hard line between corp and runner. In the real world, things are a little more porous. The corp need the best hackers to run their networks, and some of the best hackers are ex-runners who like the idea of a regular paycheck. But sometimes things run the other way, and someone on the inside makes something like this.
Corp has Tollbooth. There is a Parasite on it with 4 counters, making it currently strength 1
Runner has Ice Carver in play and runs. "All ice is encountered with its strength lowered by 1."
Is the ice trashed before the runner has to lose 3 credits? I was reading somewhere about the active player choosing the order of effects, and if it is the runners turn, could he choose to process Ice Carver effect first, then Parasite, killing it before he has to pay the 3
In a follow up question, lets say that there was only 2 Parasite counters on the ice, but the runner has Datasucker in play with 2 tokens on it. "Hosted virus counter: Rezzed piece of ice currently being encountered has -1 strength until the end of the encounter. " That says "currently being encountered", so I think you would have to lose 3 from Tollbooth before you get to use it, whereas Ice Carver says that the ice is encountered at strength -1. The Tollbooth would be trashed before its conditional ability triggered. You have two different constant effects (Ice Carver and Parasite) which combine to knock it off before the Tollbooth can force the Runner to pay credits.
Datasucker counters could not be used until after Tollbooth's ability. "When encountered" conditional abilities are resolved before there is an opportunity to trigger paid abilities.