Has 0-16 ever happenned? I remember the 1-15 Panthers but I'm not sure I've heard of a winless team. If Oakland become's the first, well, at least they'll set a milestone!

Never 0-16, the 1976 Bucaneers were 0-14 as an expansion team and the 1982 Baltimore Colts went 0-8-1 in the strike season. The 1943 and 1944 Chicago Cardinals (currently Arizona Cardinals) went 0-10 in both of those seasons. THe expansion 1960 Dallas Cowboys went 0-10-1 and the 1942 Detriot Lions went 0-11.
So, yes teams have gone winless (6 that I could find and 2 of those included a tie). There may have been a could more out there that are defunct teams from the old days but I didn't bother to dig that deep.
But your question of 0-16 is no, no team has gone winless in a full 16 game season since the schedule was increased to 16 games in 1978. Like I said, the only one in the 16 game era came in the shortened 1982 strike season (only 9 games).