Which type of injury prevention begins after an injury and is done to limit the damage caused by the injury?

Tertiary.

Explanation:

In medicine, prevention can be primary, secondary or tertiary.

Tertiary prevention refers to type of prevention that takes place ones the individual has an illness or has been injured and its goal is to soften the impact of the illness or injury that he/she suffered.

Tertiary prevention involves action to prevent sequels, to act so that the illness or injury doesn't get worse and to reduce complications.

Therefore, the type of injury prevention that begins after an injury is done to limit the damage caused by it is the tertiary.