I’ll offer brief answers to the sub-questions.
“Who owns the debt?” You might be able to find information in Canada’s financial accounts data, but all provinces are likely aggregated. Finance Quebec may voluntarily post some information on holders, but I am unaware of any sources in the public domain.
“What happens when a province falls in the red?” Canadian provincial finance is very different than American state finance. If “fall in the red” means “runs a fiscal deficit,” the province will just issue bonds.
“Is it possible for a province to no longer borrow?” Unlike American states, there are no balanced budget laws in Canadian provinces. The “limit” is the inability to float bonds in the bond markets. The Social Credit government in Alberta was forced to default in the Great Depression (1930s), and I believe that was the only post-Confederation (1867) provincial default. (It’s hard to find an authoritative reference for that statement, sorry.)
“Is there a finite anount it can borrow?” The only limit is what it can get from auctioning bonds to investors. There is no iron law determining an upper limit for that, but realistically debt levels will be compared to past history and the situation of other provinces.
A single province is relatively small when compared to aggregate borrowing/lending in the Canadian dollar financial system. Therefore, a province is unlikely to hit some aggregate “limit,” rather it is a question of whether investors are willing to allocate their portfolios towards the province. For example, if investors fear default, they will not be happy to lend, no matter how much balance sheet capacity they have to buy bonds. Discussing the aggregate lending capacity is controversial, and I am deliberately ducking that question. That should be a separate question.