Right, time doesn't slow down for them, but it would appear so for an outside observer. So would the "experience" of a particle sent in to be that it circles closer and closer for some time on the order of years and at some point when it is arbitrarily close to the center it just pops out some billion or trillion years later once the black hole has evaporated? Assuming it isn't destroyed and somehow can experience it's own time.
It would be more than a few trillion years I think, but that is the thinking unless you are a certain contentious Berkeley astrophysicist.
The particle does see itself “reach” the black hole though. And so would an outside observer if they had infinite time.
The black hole dissipating sure would make some of the experience odd. I would need to revisit my notes to make a claim about that, but discontinuities like that arent uncommon.
