Not "the Chinese", but isn't that kinda' already happening in some places? (Not "selling" their existing facility - but piggy-backing on someone else, rather than build their own)
I don't care enough to deeply explore the contract details, but programs like Miami (w the Dolphins) and Pitt (w the Steelers) sort of do that now (and there may be more, that was just OTTOMH). On a less-renowned program scale, I believe Temple and UMass have, or have had, similar relationships.
With non-football sports, I believe UTexas did something similar w their basketball arena (I think that one was more-or-less with some entity down there - maybe some sports and expo entity or some such thing), and OSU did something like that w their soccer stadium (w the Columbus Crew) and maybe their hockey arena (w the Bluejackets - but not sure about that one w/o checking on it)
The problem, if one wants to call it a problem, w PSU's situation is it is not in or near some major metro area, and doesn't have any nearby pro sports teams. So it would be hard to imagine some "public-private partnership" that would see any type of value to underwriting a facility for PSU football.