Hulu's The Handmaid's Tale has long since overtaken what happens in Margaret Atwood's novel of the same name, but the TV series can and should still have the same ending as the books. The Handmaid's Tale is currently approaching the end of its third season, having adapted all of the source material in season 1.
At the end of The Handmaid's Tale season 1, June's story ends in the exact same place that it does in the book; she's pregnant to Nick, although publicly it's Commander Waterford's child, and she's given what may be a chance to escape. In the book, she gets into a van and is taken away, her ultimate fate left unknown. In the TV show, this journey has been continued through season 2 and season 3, but while it's covered the vast majority of Atwood's book, there is still room left for more.
In The Handmaid's Tale novel, following the conclusion to June's plotline, the story continues in the distant future. Atwood switches writing forms, with the final chapter of the book reading not like June's diary entries but instead a detailed account of an academic lecture taking place in the year 2195, apparently long after the fall of Gilead. June's diaries were discovered and have since been recorded onto tape, which has allowed generations since to discover the horrors of Gilead and learn about what happened to June and the other handmaids.
The epilogue features two different speakers, Professor James Darcy Pieixoto and Professor Maryann Crescent Moon. Although not made explicit, it's clear from the text that society has returned to relative normality after the demise of Gilead, with a degree of equality existing and women no longer being subjugated into carrying children or other forms of servitude, in part evidenced by the fact a woman holds a position of such prominence.
The TV series may already be starting to think about how June's story is going to end. Although Hulu has renewed The Handmaid's Tale for season 4, it's unclear just how many years it will be able to run for. It needs to give a different ending to June's story, which may end with her eventual escape from Gilead or, more worryingly, her death, but the series can still wrap things up using this epilogue. Although it doesn't feature any characters we know, it's a great, powerful ending that contextualizes what happened in Gilead, while also having hints of how unequal even a more normalized and fair society is.
By jumping forward into the future, then The Handmaid's Tale has a means of cementing June's legacy. She's already started attempting to bring Gilead down from the inside, but true systemic change like that can often take multiple generations. It'd be great to end June's story with her having fanned the flames of revolution and helped inspire others to break free of Gilead, and then confirming that she ultimately succeeded by jumping to the future and recounting the fall of Gilead after her death. It'd keep a sense of tragedy in that June didn't live to see the true end of Gilead, while also being able to maintain holding a mirror up to the real world even with a change, and bring The Handmaid's Tale all the way back to the book that inspired it.