At the end of the episode, Mycroft explained to his parents that she was no longer verbally communicative.
That is; she would no longer talk.
The only communication she appears to respond to is playing the violin with Sherlock.
Therefore, her ability to "program" people is no longer a threat.
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Because it's the best place for her.
There is no place better set up than Sherrinford for Eurus.
As Mycroft says: There's a place called Sherrinford.
An island.
It's a secure and very secret installation whose sole purpose is to contain what we call the uncontainables.
The demons beneath the road?
This is where we trap them.
Sherrinford is more than a prison, or an asylum.
It is a fortress, built to keep the rest of the world safe from what is inside it.
As Sherrinford's residents are 'uncontainables' it is inevitable that there will be failure at some stage.
In this case Eurus' takeover of Sherrinford was a consequence of the governor ignoring Mycroft's direct orders: MYCROFT:
Has there ever been, against my express instructions, any attempt at a psychiatric evaluation of Eurus Holmes?
GOVERNOR:
Yes.
This error allowed Eurus to begin her takeover of the facility.
Finally, if Eurus cannot be kept at Sherrinford, then... where?
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Though it is not explained in details, I don't think that it is a plothole.
First of all, Great Britain does not have death penalty, so Eurus has to be contained somewhere.
Of course, we know that the British government may employ assassins at time (Mary and her AGRA team for example), but it is unlikely that Mycroft would allow that.
Remember how powerful he is in the government ("He is the government" as Sherlock describes him in the first season).
So, Eurus has to be locked somewhere.
As explained in the episode, Sherrinford is the most secure prison in the Great Britain.
It is not perfect, but perfect security does not exist.
And, as in most security breach, the problem is not the technology (the Sherrinford facility) but a human problem.
With the precedent of the manipulation of the Governor that lead to his suicide in mind, everybody will follow Mycroft's directives, Mycroft included.
Also, we may consider that Eurus is not a threat anymore .
Or at least a lesser threat.
Indeed, look at the plot of the episode.
She didn't want to have a revenge on Sherlock, or mess with him, but she was looking for brotherly affection from Sherlock in her crazy way.
As said in the episode, Sherlock was his favorite when they were children.
She got jealous of Redbeard and kind of accidentally killed him.
Accidentally because it is clear that the riddle was only a way to play with Sherlock and get his attention.
Note that she used the graves with wrong dates that Sherlock loved as a key for her riddle.
In addition, the plane game is a metaphore of her situation, estranged from people, and a call for help to Sherlock.
As a sociopath, she is a danger to people, and may harm them.
But she now restarted a relationship with her brother, and with her parents, so she is now under control in Sherrinford.
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Because, no matter how many times he breaks out, the Joker always goes to Arkham Asylum.
It's not a very satisfying answer, but the audience knows that Sherrinford is where [really] bad people go.
Why go though all the explaining that "Fordensher" is a super max security prison where all the really, really bad people go, when you already have a place that really bad people go.
To make matters worse to introduce "Fordensher" , you need to really differentiate it from Sherrinford.
What would make it different?
Sherrinford is already for people so "different" that they can't go to normal prisons, so what can Fordensher do differently enough from Sherringford that the audience could recognize the different places easily.
Take Prison Break for example (not one of my favorites
but it fits well here).
When they moved from "normal" prison to "Mexico Hell Prison" they were able to differentiate enough (even if it made no sense) that even a casual audience member would be able to tell that there was a significant difference between the first prison and the second.
You would need that kind of separation between Sherrinford and Fordensher or you risk confusing your audience.
The only other option is that Fordensher is a black hole that villains go to, and are never dredged up again for future plot usage, so there's no need to explain it.
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Interesting.
The discussion seems to presume that Mycroft and Co. made the decision to return Eurus to Sherrinford and that they, not her, were in control of the situation.
I saw very little to persuade me of that presumption.
She is clearly not only smarter and more powerful, but patient and capable of allowing others to believe, erroneously, that they are in control of her.
Why should that have changed?
Sherrinford is her headquarters, it suits her purposes, and she has them escort her back there at the end of the show, allowing them to believe that they have won.
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My question is regarding Eurus (re)imprisonment in Sherrinford at the end of S04E03.  She has been described by Mycroft as an "era-defining genius, beyond Newton."  She also managed to manipulate one of the prison guards to kill himself and his wife, just by talking to him.   Why isn't Mycroft worried that this will repeat? Why was Eurus put back in Sherrinford, where she not only managed to break free from, but also had  complete control  over it at one point?
Why was Eurus sent back to Sherrinford?
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<plot-explanation><sherlock>
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 First of all, Great Britain does not have death penalty, so Eurus has to be contained somewhere. Of course, we know that the British government may employ assassins at time (Mary and her AGRA team for example), but it is unlikely that Mycroft would allow that. So, Eurus has to be locked somewhere. As explained in the episode, Sherrinford is the most secure prison in the Great Britain. Eurus is not a threat anymore, according to Sherlock. 
Eurus is set up in Sherrinford because it's the best place for her. It's a secure and very secret installation whose sole purpose is to contain what we call the uncontainables. Great Britain does not have death penalty, so Eurus has to be contained somewhere. Eurus is not a threat anymore, according to Sherlock. Sherrinford is the most secure prison in the Great Britain. The problem is not the technology, but a human problem, says Sherlock author Mark H. Sherlock .