Unexpected Months in Hospice Have Been 'Meaningful' to Jimmy Carter as He 'Comes to the End,' Grandson Says

When former President Jimmy Carter entered hospice care back in February, his family expected the 98-year-old to only have "a matter of days" left, his grandson Jason Carter tells PEOPLE. Seven months later, the longest-living president is still watching baseball at home and enjoying time with the family that he and Rosalynn built.

"These last several months have been surprising for all of us, but it's been a real blessing," Jason says. "Both because there's been so much additional time that we've all gotten to spend together, but also because it's given us this ability to reflect on our personal relationships and experience the outpouring from around the world for him and for [Rosalynn] and for them as a couple."

And while the whole family has been moved hearing stories of how Jimmy touched others' lives, Jason notes that the former president himself feels grateful for the opportunity to glimpse at the legacy he'll soon leave behind.

"My grandfather right now is really physically limited — he's coming to the end, as is obvious by the fact that he's been in hospice — and so in that way I think he's frustrated," Jason says. "But he also has been able to experience that level of love."

Jason continues: "This is an important part of his faith journey, and it's one that you don't get to experience at any other time in your life except for the very end. And so in that way, I think this has been a really meaningful time for him, and it's been a really reflective time for him."

While Jimmy finds spiritual strength in his latest journey, Rosalynn, 96, is facing her own health challenges — in May, the former first lady was diagnosed with dementia.

"There are certainly days where my grandfather is sad that she's not participating in this reality in the same way as the rest of us, but they're still there," Jason explains. "There are a lot of different ways that [dementia] can manifest, and for her, it has manifested in such a happy and loving way, which is not surprising given the way she has lived her life and the joy that she's always felt. And so it's difficult, but it's the best possible case scenario really in that way."

Despite their limitations, Jason says, "They are definitely still there for each other."

"They are in love at home together and at peace with whatever comes. ... That love story that really defines their life continues to define it."

Jason, in many ways, appears a successor to his grandparents' legacy.

He chairs the Carter Center — the human rights organization that Jimmy and Rosalynn founded after leaving the White House — and followed in his grandfather's footsteps as both a Georgia state senator from 2010 to 2015 and the state's Democratic nominee for governor in 2014. He began his public service career in the Peace Corps on the advice of Jimmy.

But Jason rebuffs being described that way, insisting that he's only one of countless individuals whose stories reflect the hard work of his grandparents. His exact words: "There's millions of successors."

Jason asks PEOPLE if he can share a story before hustling to another appointment.

He says that one time at a McDonald's in Cordele, Georgia, a woman ran up to his grandfather and — fumbling her words — shouted, "Oh my God, do you know who you are?" Jimmy responded simply: "Yes. Who are you?"

Mortified, he says, the woman found it in herself to laugh along with the group at her bizarre question and pose for some photos with the former president.

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The random memory — one of many funny and ultimately inconsequential encounters involving Jimmy over the years — stands out to Jason as he reflects on his grandfather's inspiring sense of direction throughout his career. Not because Jimmy responded with a perhaps accidental level of sass, but because of the metaphor buried within the dialogue.

"The answer to that question, 'Do you know who you are?' And he's like, 'Yes.' I think that's actually true for him, and that's not true for everybody."