Yes. Some charities "co-own" their service dogs, but not Pawsitivity, and we will never forcibly "take back" the dog (even if the handler passes away, the dog can be kept by the family as a loving and supportive pet).
Note that all rescuing and training is funded by donations from past donors--your donations will help Pawsitivity rescue and train future dogs and each participant "pays it forward". Once we match dog and person, the dog is yours--we will spend six to twelve months in rehabilitation and training, but the dog is yours the whole time. :-)