So, Sentient Species moved to Host Planet, and built a Structure, made of Solid Unobtainium, in order to make livable space for them. The basic purpose of the Structure was to provide shade for Sentient Species, who would be unable to live under the direct light of the local sun. Later, Sentient Species went away or died out, and only the Structure remained.
In this case, it seems to me that the purpose of the Structure was to provide an ecosystem similar to that on the Home Planet of Sentient Species. So life would have to be possible Under the Structure, though it could be the case that it would be impossible for Host Planet life forms to live there. The question then would be, once the Structure is abandoned and no longer maintained, would exo-life from Home Planet be able to thrive, or would it die out, leaving a dead, uninhabitable part of Host Planet - Underthestructuristan?
Roughly, if the ecosystem under the Structure needed conscious intervention from Sentient Species, then it will eventually die out. Otherwise, it will probably last as long as the Structure is able to resist erosion and biodegradation.
Sentient Species, and whatever species it cultivated under the Structure would, however, be blind. Unless, of course, their problem wasn't exactly sunlight, but:
a) a specific wavelenght, for some reason absent in Home Planet but present in Host Planet; or
b) intensity, if they can resist light, just not as much light as that provided by Host Planet's sun.
In these cases, Solid Unobtainium doesn't need to be totally opaque; it could be translucid or event totally transparent except for the forbidden wavelenght. Then maybe Sentient Species can "see", but not the same wavelenghts that are visible for us (and/or for Host Planet animal life), and maybe it is exactly the visible spectrum of Host Planet that is deatly for them. Ie, they need light, just not the same light as Host Planet life forms need. If this is reciprocal, then neither life under the Structure can spread out of its limits, nor life from the rest of the planet can invade Underthestructuristan, not at least before a long and complex process of evolution. If it is unilateral, then life from the outside will creep in, and eventually replace the exo-ecosystem.
In case the problem is intensity, moreover, they could use a different solution: settling by the polar region of Host Planet, where light intensity would be much lower than closer to Equator.
Also, besides its optical qualities, Solid Unobtainium would be different concerning whether it was conceived in order to be non-biodegradable under Home Planet conditions (in which case it could be vulnerable to Host Planet's microbiosphere), or, on the contrary, invented to be resistant to Host Planet's environment, while it would have to be maintained to resist Home Planet microlife.
But, beneath all this, lies the issue: you have had us agreed to suspend our disbelief concerning the nature of this strange material that was used to build the Structure. If you now try to give us too much scientific or "scientific-ese" explanations for what happens under the Structure after its builders are gone, you risk have us requestioning the whole nature of Solid Unobtainium.