Dugard, 29, has been surrounded by her two daughters, her mother, her sister (who was just one when Jaycee was abducted) and other family members, and has been undergoing psychological counseling.
Very little is known about how she and her family have been coping, and about her nearly two decades in captivity since she was grabbed from a bus stop in broad daylight in South Lake Tahoe, Calif. in 1991, allegedly by Phillip Garrido and his wife, Nancy Garrido.
Both have pleaded not guilty to charges including kidnapping and rape. Authorities say Garrido fathered Jaycee's two daughters, who are now 15 and 11.
The Garridos are accused of keeping Jaycee and her daughters in a backyard maze of tens and sheds all these years, at their Antioch, Calif. home.
Investigators for signs of two other abducted girls, Michaela Garecht, who was nine when taken in 1988, and Ilene Misheloff, who was 13 when she was grabbed in 1989.
Now, a lawyer hired by Jaycee's family says she would probably testify against the Garridos when the time comes.
"I'm confident in saying that, if this case does proceed to trial, Jaycee will, in all likelihood, be a witness for the prosecution," McGregor Scott told "Early Show" co-anchor Maggie Rodriguez. "She's aware of that, and understands that. That day is a long ways away from right now, so she's got a lot of time to continue with the mending and the healing and the rehabilitation she's going through now."
More on the Jaycee Dugard investigation on CBSNews.com
New Signs of Body Burial in Garrido Yard?
More Bone Fragments Found at Garrido House
Girls Other Than Jaycee in Garrido Yard?
Sources: Inmates Threatening Nancy Garrido
Dr. Phil: Dugard, Kids Face Long Road
Jaycee's Terror as Her Ordeal Began
Jaycee's mother, Terry Probyn, has issued a statement saying, "All of us are doing very well under the circumstances. What we need most right now is to be allowed to become a family again within a zone of privacy and security."
Scott told Rodriguez privacy is a primary concern of the family's, but Jaycee's relatives also want her case to give hope and encouragement to other families of abducted children.
Scott says Jaycee is doing "remarkably well," under the circumstances:
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