[Numenorean]

Well met Kuru, Saureg & Tuor, interesting lines of thought you have all had here, things that I too have pondered at length. Sorry to jump in after you have probably moved on from this, but like Kuru has already said:

My current curiosity is over the nature of Morgoth's power over Húrin's life. If Morgoth had kept Húrin in that state for a much longer period of time, would Húrin eventually have turned into a wraith of some sort?

I would not find that too difficult to believe at all. Indeed, was Húrin already a wraith of sorts from the moment that Morgoth "set his power upon him"? The fact that Húrin somehow survived for 28 impossibly harsh years upon a bleak and desolate mountainside, without food nor any natural sustinence leads me to believe that he was infused with supernatural life and power - directly from Morgoth himself . No small thing as under 'normal' circumstances he should have died within weeks/days of being chained to Angband. Through Morgoth he also saw and heard things that were far beyond his ken to do so, again this indicates he was something other than simply human, he was by despicable extention of this theory, an unwilling ancillary of the Bauglir himself.
Saureg:

I am under the impression that Húrin was released from bondage with his death. I also believe that the curse of Morgoth only extended to the affecting the life of the one being cursed and nothing more.

The first point you raise here does not necessarily exclude the possibility that Húrin was or could be a wraith. Perhaps if he had not taken his own life he may have endured a Sméagolesque unaturally long lifespan, who can really say? In the past I always baulked over Húrins suicide, but I have since come to believe that he did it as a direct act of defiance and faith. When Morgoth says to him “…beyond the Circles of the World there is Nothing.” It seems clear that it is an attempt to make him fear death and not accept it as Ilúvatars Gift to Men. Thus by ending his own life Húrin both defies Morgoths bleak statement and reaffirms his own faith in the Valar, his choice of place to commit this act – the Westernmost shores of Beleriand – is also significant.
Your second point Saureg – regarding the scope of Morgoths curse only affecting Húrin is something I disagree with. Here are the exact words of the curse:
“But upon all whom you love my thought shall weigh as a cloud of Doom, and it shall bring them down into darkness and despair. Wherever they go, evil shall arise. Whenever they speak, their words shall bring ill counsel. Whatsoever they do shall turn against them. They shall die without hope, cursing both life and death.”
Unfortunately this is exactly what does happen, specifically to Túrin but also in degrees to Morwen and Nienor. Húrin may have been the catalyst but his family - his loved ones - bore the very real consequences of the curse to their bitter ends.

It seems that it is feasibly within the power of both Vala and Maiar to affect and alter the lifespan of Erus children, if they were inclined to do so. This is why, as Kuru puts it:

Morgoth and Sauron were able to do what they did is that they had tried to break as many ties with Eru's restrictions as possible, this could include not meddling with the lifespans of the Children.

Sauron and Morgoth obviously did not feel bound to obey the rules of governance that Manwë and his train did, therefore their power, when laid upon mortals, changed the natural order of the subjects life – Húrin, the Nazgûl, Sméagol even Bilbo all lived far longer than they should have as a direct result of being bestowed with Ainuric power. Sauron and Morgoth took the power of doom and warped it to their own evil purpose, regardless of the effect it had or the rules they broke in doing so. I feel that other powerful Ainur could also have done this, but for the most part they seem to have obeyed the will and restrictions of Eru - unless given special dispensation to act, as seen in the case of the Peredhil that Saureg has just quoted:

Manwë gave judgement, and he said: "In this matter the power of doom is given to me…”