I think it's pretty clear you're going to lose all games. PS+ is a rental service. Steam is a rental service. Want to keep a game? Buy it on disc, problem solved.
The reasoning is that Sony doesn't own these games. There are hundreds of publishers and 3rd party studios involved, so it's likely that there's no legal way for Sony to basically hand out free digital copies.
Anyway, it's likely that when they shut down PSN for a console, it's because it's so old that almost nobody is using it anymore. Looking at how Live works, the OG Xbox was still active on it until 2010.