After death, is there a final chance to be saved?

No.

The picture in the Bible is that the rich man went to Hades, Lazarus went to the bosom of Abraham, and a great gulf was fixed. "You cannot come from there to here. He cannot come from here to you" (Luke 16:26). It's over.

There is no indication in the Bible that there's a purgatory or that there's a chance that God would let you be saved.

I can think of one exception, and it's only an exception if you conceive of it a certain way—namely, infants. I believe that infants are saved, that they don't go to hell who die.

It's a long argument. But when people ask me, "So, are they already saved? Are they born again? Have they believed? You believe that regeneration happens through faith. They haven't believed yet, because they're little babies. So how are they saved, if they're not regenerate since they haven't believed? Where do they get saved if you say they're saved?"

And I back away from those questions because my answer to why I think they're saved isn't based on how they get saved.

I speculate about God instantaneously causing little babies to come into their maturity when they die—I don't know what that would be, a 35 year-old mentality or something—and that immediately they are believers. But all that is speculation, and that's another issue.

I think God's justice in Romans 1:18-21 implies that babies who do not have the resources to construe revelation will not be held accountable for their fallenness. They will be saved by Jesus.

But for everybody else, there is only one opportunity to be saved. And that is: Believe on the Lord Jesus now, and you will be saved.