I don't think it'll surprise you that it depends very much on who the creditors and debtors are, and the circumstances of the transition. Infamously, the US during Reconstruction, by means of the 14th Amendment, explicitly disavowed all the Confederacy's internal and external debts for what seem like quite obvious reasons. The Bolshevik government similarly disavowed Tsarist debts for much the same reason (Trotsky, in his 1930 autobiography: "And later, after the victories of the revolution, the decree of the Soviet of People’s Commissaries, issued on February 10, 1918, declared all the Czarist debts annulled. This decree remains in force even to this day. It is wrong to say, as some do, that the October revolution does not recognize any obligations: its own obligations the revolution recognizes to the full. The obligation that it took upon itself on December 2, 1905, it carried out on February 10, 1917. The revolution is fully entitled to remind the creditors of Czarism: “Gentlemen, you were warned in ample time.”). However, the future Soviet government was plenty willing to use the issue of debt as a bargaining chip, as is the nature of a debtor: if you owe money, you have a perverse leverage as your creditors tend to be interested in recovering it. Over the course of 1933-35, they attempted to trade assumption of some debts to the United States in exchange for diplomatic and trade benefits and further loans, although the agreements eventually broke down (The Roosevelt-Litvinov Agreements: The American View, Donald Bishop for further discussion on this).

Slightly more complicated is, as you allude to, the former Soviet bloc. A previous answer on the sub by /u/kieslowskifan and /u/terminus-trantor may be of use: https://www.reddit.com/r/AskHistorians/comments/3o3fem/what_happened_to_the_soviet_unions_debt_or_east/

Essentially, Russia took on the debt and assets of the USSR in much the same way that it assumed the international person of the USSR. West Germany consented to assume the international debt of the former GDR with the exception of debt to the rest of COMECON. Compared to the disavowals above, West Germany was by no means in a controlling position in these negotiations: the United States was relatively untouchable morally and physically, and Lenin's Bolsheviks were in any case in no position for much international trade due to the war, let alone the ideological issue. Meanwhile, Kohl's FRG was a second tier party in it's own negotiation, which was restricted by the interests of the US and USSR, as well as pressure from France and the UK; moreover, the FRG was deeply involved in international trade, meaning that some assumption of debt would be necessary to maintain relations and international credit-worthiness.

With regards to internal debt, the East German Mark was convertible to West German Marks at 1:1 for wages and small savings, 2:1 for large savings, investment, and debt - very roughly speaking, substantial assets were written down by 50%. I can't speak to what this would mean if you were an East German with say a mortgage, but, since the 1:1 conversion was extremely generous to the value of the East German Mark, the immediate, short-term purchasing power of the average East German rose significantly.

Returning to the original question, the trend for debts during regime changes is that they are discharged to the greatest possible degree. In your hypothetical, New Canada would presumably have a hard time writing off all the USA's internal debts if they wanted the population to stay happy (getting your savings wiped out would not exactly endear you to the new regime), but conversely, there's quite a lot of American internal debt, to say nothing of foreign, so I think you'd expect a lot of it to be cancelled out of financial necessity. What would be honored and cancelled would be at the end of the day a political calculation.

e: Unfortunately I came across this late, but there's a very in-depth discussion of debt succession by way of Rhodesia here: https://www.mcgill.ca/mjsdl/files/mjsdl/terry_1_0.pdf