Different aircraft have different system configurations, so this is a bit 'generic'.
Assuming the aircraft has two ADCs, one for pilot and one copilot display, it will also have two pitot-static sources. Typically there will be one pitot source on each side of the nose, and two static sources on each side; the static sources may be part of a "pitot-static" combined probe, or the static sources may be flush-mounted to the fuselage separately.
The sources will be connected such that each pitot source is connected to a single ADC, and a pair of static sources will be connected (one left, one right) to each ADC.
Therefore each ADC is connected to an independent set of air data sources.
If either data source set has a failure (say a blocked port) then the readings from that system will go 'strange' and may be detected automatically or by the pilots. Depending on the design, some aircraft may be able to switch to a back-up source (some have 3 or more ADCs) or may be able to switch the display source so that all the pilot and copilot displays use a common, valid, ADC, or the procedure may simply be that the pilot/copilot with the 'good' ADC flies the aircraft.