In Campaign, when a deployment group is defeated it is returned to the Imperial players hand of open groups. Villains cannot be redeployed from your open groups after being defeated.

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Villains:

Imperial allies are referred to as villains. They follow all of the same rules as allies, in addition to the following:

• Once gained as a reward, villains (such as “Darth Vader”) can be brought into any mission as an open group.

Open Groups:

• When the last figure in a group is defeated, the Deployment card returns to the Imperial player’s hand of Deployment cards.

Allies:

• When an ally is defeated, it is removed from the map and cannot be redeployed for the remainder of the mission. The ally may be used in future missions following normal rules.

Despite not being redeployed, do Villains still count as being in your open groups after defeated for the purposes of Inspirational, etc?

When non-unique groups are defeated, they return to your hand of open groups.

So, when a unique group (a villain) is defeated, the deployment card is out of the mission. It is thus not available for the abilities of the Nemeses class deck.

So, No. (Which is why you might not even deploy all of your villains during a mission.)

Defeated said:

During a campaign, when the last Imperial figure in a non-
unique group is defeated, the Deployment card is returned to
the Imperial player's hand and can be optionally deployed later
in the mission.

(Emphasis from the RRG.)

Awww shucks, I was hoping it encouraged the IP to deploy them early and still benefit from them once defeated. Thanks a1bert!