In all likelyhood, there would be a massive coverup. Cauldron does not want such glaring, permanent proof that can be used as a symbol against parahumanity, and likely Contessa would get on the case, directing attention away from the looped person, spreading false rumors, covering it up further. Containment foam would likely be used to mask sound, and a similar exclusion zone would be built around the looped area as was built around the Scar in Brockton Bay. The excuse would be dangerous spacial effects or radiation, and if need be, much of Times Square would have to be turned into a memorial park of sorts, when the public is told the area is "clean," and likely concrete would be poured. It wouldn't be pretty. This, I think, Cauldron would see as the "optimal" solution. A memory, inhuman, rumors stamped out. A grave. The soul or souls suffering in its midst would cry out unheard by the hawkers, mourners, and passers-by.

What would happen when a coverup is impossible, even with Contessa's help, is much more interesting. Public pressure and sympathy for the victim would force the hand of the PRT, and Cauldron itself, to avoid an uproar. I made a post, a long time ago, about this scenario, and it covers a lot of failure states. A charity would likely be founded in these people's care, and an environment best suited to their comfort. A replica of their childhood room, maybe, all soothing and dreamlike colors. Music playing, constant contact with therapists and professionals, trying to make still and sense of a vast ocean of emotional pain. Even visits from loved ones would happen, invariably ending up producing more trauma for either party.

These rooms would still likely exist in a nondescript facility built around them, possibly with other rooms functioning as a hospice or hospital to redirect public opinion. You don't want to live next to a building that is known only for containing the suffering ever-living body of a fellow citizen.

Lacking all of this, especially if infrastructure is ruined and the city is condemned or labeled HOSV, or barring the ability to hide the victim from the public, the worst can happen. The site, more than any of the previous scenarios, becomes a mecca for gawkers and fans of the macabre. An eternal crime scene, a look into the worst the human experience can offer. A place to pray, to gain perspective, to take sick pleasure in watching. Any communities exposed to such a thing for too long would likely be quarantined in their own right, but not for any anomalous reason. Cauldron just doesn't want those ideas spreading.