If you made it through Sam's feces-themed montage in the Season 7 premiere of Game of Thrones, then you saw Ser Jorah Mormont's greyscaled hand reach out to the aspiring maester to ask if Daenerys Stormborn had come to Westeros yet. This moment not only revealed where Jorah has been since Season 6's fifth episode, but it also led to the theory that Sam could save Jorah on Game of Thrones. Sam has already been investigating dragonglass in order to help Jon Snow fight the white walkers and if this theory is to be believed, his research just may save Jorah's life too. And how perfect for Jorah that the very thing that could save his life could come from the birthplace of his queen and love Daenerys Targaryen — and how convenient that she just returned there for the first time in the Season 7 premiere.
While you were probably distracted by the discovery made by Sam (and Gilly!) that the Targaryen castle Dragonstone is built on dragonglass and that Sam will be passing this essential intel to Jon in Winterfell, other viewers were busy doing their own maester-like studying. By reddit users, like StormSS, focusing in on the pages of the book that Sam took from the restricted area of the Citadel's library, fans started the theory that ingesting dragonglass could be the cure for greyscale. Here's a photo of the page that Sam was reading during his Dragonstone discovery.
And if you look to the page on the left, you can see that the book discusses dragonglass being a cure for some unnamed illness, as StormSS documented in this photo.
While the book never explicitly states "greyscale" and this text implies that dragonglass might not be the most practical cure for whatever ailment it is referencing, grayscale being the topic of this passage still somehow doesn't feel like too far of a stretch. Plus, the possibility that the book is referring to greyscale gets some support from Reddit user Beastmodekait, who noted, "Considering the only person to be cured that we've heard of was Shireen and the mine of dragon glass [sic] is at Dragonstone, it seems likely!" Although Stannis claimed that the maesters, healers, and apothecaries that he brought to his daughter when she was a baby stopped the greyscale from spreading, could it really just be a coincidence that Shireen was raised at Dragonstone? Furthermore, the Shireen connection makes a lot of sense when it comes to Sam and Gilly being involved if you go back to the second episode of Season 5, "The House of Black and White."
In the Season 5 episode, Shireen is at the Wall teaching Gilly how to read while Sam is present. Gilly asks Shireen about the greyscale on her face since two of her sisters had it. Shireen notes that people were brought in to help cure her and "whatever they did, it went away." Even if Sam doesn't end up remembering this exchange, it's almost guaranteed that Gilly would remember it, allowing the pair of them to make the connection between greyscale and dragonglass — because let's not underestimate Gilly's potential contribution to curing Jorah.
In an interview with Huffington Post, Sam actor John Bradley discussed Sam and Jorah's storylines coming together and implied that if Sam discovers a way to help him, he would do it. Bradley said:
Bradley mentioned a "link that connects the characters" and that may be Jorah's father — Jeor Mormont. Jeor was the Lord Commander of the Night's Watch when Sam and Jon first joined the brotherhood. As Bradley said, Sam would need the "right motive" to help someone and knowing what a good man Jeor was would certainly be an incentive to save Jorah.
With all of these connections, it almost seems unlikely that Sam and Gilly wouldn't save Jorah. While that doesn't necessarily mean that Jorah will have a happy ending, it would be absurdly fitting for his salvation to lie in Daenerys' birthplace — and perhaps provide him enough joy to get him through whatever is left of his pining existence.