 In the original cut of the film, there was a scene in which Eric Draven has a  fight with Funboy in Funboys apartment before killing him.  It goes like  this: Eric knocks the straight razor from Darlas hand.  Eric makes Darla  sober by magically siphoning morhpine from her blood.  Darla leaves.  Funboy  wakes up in the bathtub and grabs the razor.  He attacks Eric and cuts his  hands and torso.  Because Eric has weakened himself by getting the morphine  out of Darla, he cannot heal properly.  (This would have been explained by  the Skull Cowboy, but those scenes were also cut.) To cover the wounds, he  wraps them in black electrical tape.  This explains why his hands and stomach  are wrapped up later in the movie.