Dropped players change "card" w/ new team?

Howdy,

Does a dropped player change his "card" when he's picked up by a new team or does he continue with the card he had while playing for his first team?

In which format?

Howdy,

Mysterycard league. Specifically in my case, the 70s.

A player keeps the same year regardless how many times he's dropped or how many teams he plays for in a season.