From the Friday the 13th Wiki:
Paul's fate was more explained in an interview with Peter Bracke,
author of Crystal Lake Memories: The Complete History of Friday the
13th, in the Friday the 13th Part II DVD features. There he reveals
that there was an unused ending in the movie. After Ginny questions
where Paul is, the scene switches to Mrs. Voorhees' head, which opens
its eyes and smiles, indicating that Jason had killed Paul. But when
they filmed it, they thought it looked too silly. So it was taken out
of the movie.
From the same source, going by the available information in this movie and its sequel:
Rumors say that Paul survived and is probably safe at home, laying
low. Though no proof is given, to support the rumors. Since Ginny had
blacked out during the last attempt, Paul may have fought off Jason to
prevent him from killing Ginny. Depending on who had the upper hand
Paul could have fought off Jason enough to run away afterwards, or was
killed defending Ginny and his body was taken by Jason, but at the
beginning of Part III, a news broadcast reports the body count at
eight, thus excluding Paul from this count, possibly meaning that Paul
survived the ordeal. However, the news man reporting 8 corpses were a
goof as only 6 corpses were found while the other 2 were at a shack
along with the corpse of Alice Hardy and the head of Pamela Voorhees,
however Paul's body was not seen in the shack at the end of the movie.