There's a lot of ways this could end.
Bear with me here.... This is just a personal prediction!
A small amount of money continues to slowly trickle into the program. Here we go:
Over time, some gun owners decide to participate, mostly turning in the lower-end stuff, for example a rusty mix-master M1 Carbine that bubba has done dirty, the real junkers you would be scared to take to the range. In this case, these low-end junkers are compensated fairly because they are valued at a fixed rate (Say maybe $500) and the owner paid next to nothing for a beater they probably make a nice profit on it they can use to buy something new. If someone or a business was stock piling junkers, they probably actually make a bunch of money from the situation.
Following this, the LPC call the buyback a big success, they take some photos with the stuff they collected, throw out some stats that sound impressive, and they show they've been "removing deadly weapons from the street" to their base when the next election comes around. In reality, most gun owners still have their stuff, and what was turned was mostly crap and a tiny drop in the bucket.
Following this, the Liberals and Conservatives each continue to use gun ownership as a wedge issue, and the charade continues for several more decades. Neither side is completely satisfied, the country remains divided on the issue.
If the Liberal's stay in power, they continue to trickle out more buybacks, they continue to find new models or things to ban slowly, more minor tweaks in the law, and they know full well that if they actually confiscated everything at once and the issue becomes irrelevant, they can no longer use it as a wedge issue, so they don't rush any of this.
If the Conservatives gain power, they do a partial rollback of the Liberals policy, but it's not exactly what gun owners desire either, they do a little bit at a time and keep telling their base that if they keep them in power they may do more for them. For example, they stop the buyback, but they don't end the handgun freeze unless they win a few more elections in a row. They keep make promises to "help law abiding gun owners" while also not completely undoing everything or creating an entire new logical balanced system of gun ownership that would put the issue to rest.
I know, it's hard to predict, and feel free to tear my prediction apart, but that's exactly how I see this going and the most likely course of action I could see happening in coming years / decades having followed this issue going back to the end of the Second World War when the registries began in this country. I highly doubt either side is going to satisfied anytime soon.
Side note: the situation will likely be taken advantage of by firearms businesses and experienced used gun buyers who are buying up guns that they know will be banned for super cheap, and government will end up paying them a "fixed rate" which is like much more than they actually paid in these cases, since they don't have the resources or expertise to actually rate and give fair value for each gun, which will be one of worst aspects of the entire program. This happened in both the UK and Australia, and some people made a lot of money doing it.