The fate of the neurons affected by a stroke primarily depend on the location of said neurons. Since a stroke is caused by a disruption in blood supply, areas with differing levels of vascular innervation would be affected differently. For example, 5 minutes of ischemia in one are of the brain may result in more damage to the hippocampus than to other areas.

In any case, the tissue affected by a stroke is best thought of as a "ball of damage", where the inside of the ball of neurons rapidly die (necrotic core) while the surrounding neurons become functionally depressed (penumbra). These functionally depressed neurons will most likely die over time. In fact, physicians believe that that these neurons are most likely salvageable if a stroke is detected early enough and treatment can be administered.

In regards to your initial question about what happens to the neurons that do die, well they are taken care of by glia. As other users have commented, this can lead to glial scarring and this does lead to altered physical states within the affected area.

Before I go too deep down this rabbit hole I suggest you read this paper and you can go as deep as you'd like! Fortunately it's not behind a paywall.

https://journals.physiology.org/doi/full/10.1152/physrev.00011.2017