I see this as a fairly common misconception. None of the Chara/Frisk/Player party are part of the Delta Rune Prophecy in either interpretation of it; not as the free-er or the destroyer.
First, here is, word-for-word, the prophecy, as written on the Waterfall texts.
Now, of course “seen the surface and returned” could apply to both of them, but it in fact only applies to one of them.
That’s because the Delta Rune is directly connected to the prophecy by the people in the Underground. Specifically, the “winged circle”.
The winged circle is especially important, as no one seems to quite know what it could be, but they have named the winged circle an “angel”.
It is important to note that the “Angel of Death” interpretation is not part of the original prophecy, but born of pessimism that’s slowly overtaking the Underground.
However, some people use this line as evidence that Chara never wished for monsters’ freedom, and only wished to “bring them destruction”.
The prophecy itself – “and the Underground will go empty” is vaguely worded, to be sure. The fact is, the Underground does go empty in both senses…at the same time, and from the same person.
This person brings destruction to the world, frees the monsters from the mortal realm, and frees the monsters from the Underground.
This person, as many of us know, is Asriel Dreemur.
The form he takes during the second part of the fight is his truest form after taking the souls; not the generated form it was before. This form is the only form in the entire game that fulfills the delta rune imagery.
Of a winged circle. The “Something else” in the imagery was the Soul of Asriel, made up of every soul in the Underground.
Asriel “freed all monsters from the mortal realm”.
Asrielbecame a “harbinger of destruction”.
Asriel freed them from the Underground.
We are given two different interpretations – of an “angel of death” and an “angel of freedom” because when we first see the delta rune in Asriel, he’s attacking us at full power. We should recognize the rune at that time and at first believe the “angel of death” must be the true interpretation, then realize later he is in factalso the “angel of freedom”.
Chara never manages to completely empty the Underground; every time, Alphys, Monster Kid, and every non-attacking citizen NPC (quite a few monsters!) make it to an escape route and are never caught.
Chara has also never been associated with the winged circle or delta rune, even at the no-mercy ending where the opportunity could have arisen. They are not part of the prophecy, and the prophecy is not “proof” they are destruction itself.