Velocity and Capacity
20% of the team left during the particular sprint. Does the velocity change?
It is likely that your velocity will change because the team's capacity has changed, but a lot depends on the work that the team has planned for the Sprint and the cross-functional composition of the team. As a rough planning value, you should probably assume that you will lose 20% of your capacity for the current Sprint, but the Development Team should determine the appropriate fudge factor to apply during Sprint Planning. It may be more or less than 20%, depending on the work selected for the Sprint.
Over time, your velocity will either smooth over a one-off blip in team capacity, or trend towards a new average if this is the new norm for the team. Either way, this sort of trailing metric is essentially self-correcting. Changes in the team or the process will generally result in changes to velocity, and that's as it should be. As long as you aren't using it incorrectly as a productivity metric, you should allow the data to correctly reflect these changes rather than forcibly recalibrating the metric.
Velocity and the Sprint Goal
The correct use of velocity is to determine whether all the work needed to meet the current Sprint Goal can fit within a single Sprint. If Sprint Planning results in a Sprint Backlog that exceeds the Development Team's expected capacity for the current Sprint, the work selected (and possibly the Sprint Goal) will need to be renegotiated.
In other words, it is unlikely that a team of 6 will have the same capacity as a team of 8, so less work should probably be selected for the current Sprint. Velocity (with appropriate fudge factors) can provide a sanity check for the team and help avoid oversubscription, but in the end the Development Team is committing to achieving a Sprint Goal rather than delivering a set number of story points.
Focus on the Sprint Goal, not the velocity forecast. If you don't have a Sprint Goal, then fix that process problem ASAP. Focus on delivering the Sprint Goal, and let the velocity metric speak for itself.