I found out some stuff about Jucika after reaching out to László Dluhopolszky aka Dluho, an editor and cartoonist who worked at the Ludas Matyi magazine that published the strips. Here's what he told me.
Jucika's creator, Pál Pusztai has no descendants. He had a wife but no kids and we don't know what became of his wife after his passing in 1970.
The original Jucika strips don't exist anymore. Pusztai's wife allegedly hated Jucika so much that she threw the drawings into a fire after her husband's death. This is supposedly because Jucika was possibly based on a real person that Pusztai's wife was jealous of. Only one half-finished strip was found in Pusztai's drawer that the magazine published months after his death.
There was an initiative by another magazine to continue Jucika with other artists but this idea was scrapped.
Dluho was surprised by Jucika's boom in internet popularity and is currently researching the strip's copyright status. He says he can take the matter all the way to the government and knows a company that could restore the original strips from the old magazines. He also has connections in Japan in case the Japanese would be interested in a Jucika collection. Some of Pusztai's old friends are still alive and they might help out too.