The exoplanet would be destroyed. The average surface temperature of a neutron star is in the order of hundreds of thousands of degrees, this would vaporise almost any material that came in contact with it. Should a planetary body in orbit around the star fall into the neutron core it would be incinerated rapidly and explosively.
The likelihood that such a body would survive this kind of event is very low. Any bodies around the star would be greatly disrupted during the supernova event with a large proportion potentially being thrown from their parent Solar System. The search for these free-floating planets is underway in an attempt to confirm these theories.
Got a question for us? Send it into email@example.com and you could see it featured in All About Space – available every month for just £3.99. Alternatively you can subscribe here for a fraction of the price!